SM 2. Date: Section: Objective: The Pythagorean Theorem: In a triangle, or

Size: px
Start display at page:

Download "SM 2. Date: Section: Objective: The Pythagorean Theorem: In a triangle, or"

Transcription

1 SM 2 Date: Section: Objective: The Pythagorean Theorem: In a triangle, or. It doesn t matter which leg is a and which leg is b. The hypotenuse is the side across from the right angle. To find the length of the hypotenuse: Steps for solving the formula for c: To find the length of a leg: Steps for solving the formula for a or b: Shortcuts: To find the length of the hypotenuse: To find the length of a leg:

2 Examples: Find the length of the missing side of each triangle. Write answer as exact and rounded to the nearest hundredth. d) e) f) g) h) i) j)

3 Distance Formula: Example: Find the distance between ( 1,5) and ( ) 7, Plot the two points on a graph and 2. Draw a right triangle with connect them with a segment. your segment as the hypotenuse. 3. Figure out the lengths of the legs. 4. Plug into the Pythagorean Theorem. -or- Use the distance formula (but be careful with your negatives!) ( ) ( ) 2 2 d = x x + y y

4 Examples: Find the distance between each set of points. d) ( 5, 6 ) and ( 1, 2) e) ( 4, 7 ) and ( 9, 3) f) ( 2,3 ) and ( 5, 7)

5 SM 2 Date: Section: Objective: Review: How do you find a missing side length in a right triangle? Use the to find the length of the hypotenuse for each right triangle. Express your answers in simplest radical form. There are 2 common types of right triangles with special patterns that can be found using the Pythagorean Theorem Right Triangles: Legs are Hypotenuse= Examples: Find the value of each variable.

6 d) e) f) g) h) Right Triangles: Hypotenuse= Long Leg= Examples: Find the value of each variable.

7 d) e) f) g) h) i) j) k) l)

8 SM 2 Date: Section: Objective: Trigonometry: Trigonometric Ratio: 3 main or most common trigonometric ratios: 1) sinθ = 2) cosθ = 3) tanθ = Adjacent means next to θ (the angle you are focusing on) Opposite means across from θ (the angle you are focusing on) Hypotenuse is the side across from the right angle A common way to remember this is: Steps to find the trigonometric ratios 1) 2) 3) 4)

9 Examples: Find the exact values of sin θ, cos θ, and tan θ. No matter how big the triangle is, the values of the trigonometric functions for a certain size angle will remain x y z the same. For example, in the diagram below, tan 27 = = =. The value of the tangent is the same in all a b c three triangles even though they are different sizes. The same is true for the sine and cosine. Examples: Use a calculator to approximate each value to four decimal places. Make sure your calculator is in degree mode. a) sin 27 b) cos 27 c) tan 27 Steps to find the missing side of a right triangle if you know an angle and one other side: 1) 2) 3) 4)

10 Examples: Write an equation involving sine, cosine, or tangent that can be used to find the missing length. Then solve the equation. Round your answers to the nearest tenth. d) e) f) g) h) i) j) k) l)

11 Examples: Draw and label a triangle to illustrate the situation. Find the length of the missing side and give the values of the requested functions. a) Given 7 sinθ =, find tanθ and cosθ. 25 b) Given 15 tanθ =, find sinθ and cosθ. 8

12 SM 2 Date: Section: Objective: Inverse functions: When do you use inverse functions? sin ( ANGLE ) cos( ANGLE ) tan ( ANGLE) = RATIO OF SIDES 1 sin ( RATIO OF SIDES) = ANGLE = RATIO OF SIDES 1 cos ( RATIO OF SIDES) = ANGLE = RATIO OF SIDES 1 tan ( RATIO OF SIDES) = ANGLE Examples: Find the measure of the indicated angle to the nearest tenth of a degree.

13 Solving a Triangle: Figuring out the lengths of all three sides and the measures of all three angles of a triangle. DRAW AND LABEL A TRIANGLE (Label the pieces you know with numbers and the pieces you don t know with vairables)! Decide which of these choices your triangle is like. Then follow the instructions. Show work! If you know the measure of one angle and the length of one side, o To find the measure of the other angle: o To find the lengths of the other sides: If you know the lengths of two of the sides, o To find the length of the other side: o To find the measures of the angles: Examples: Solve ABC. Round answers to the nearest tenth. Show all your work. a) b)

14 c) d) e) m A = 72, c = 10 f) m B = 20, a = 15 g) b = 4, c = 9 h) a = 7, b = 5

15 Examples: 1) Draw and label a triangle to illustrate the situation. 2) Find the length of the missing side. 3) Give the values of the requested functions. 4) Give the measure of the angle to the nearest tenth of a degree. a) Given 4 sinθ =, find tanθ and cosθ. 5 b) Given 12 tanθ =, find sinθ and cosθ. 5

Unit 2: Trigonometry. This lesson is not covered in your workbook. It is a review of trigonometry topics from previous courses.

Unit 2: Trigonometry. This lesson is not covered in your workbook. It is a review of trigonometry topics from previous courses. Unit 2: Trigonometry This lesson is not covered in your workbook. It is a review of trigonometry topics from previous courses. Pythagorean Theorem Recall that, for any right angled triangle, the square

More information

Objectives: After completing this section, you should be able to do the following: Calculate the lengths of sides and angles of a right triangle using

Objectives: After completing this section, you should be able to do the following: Calculate the lengths of sides and angles of a right triangle using Ch 13 - RIGHT TRIANGLE TRIGONOMETRY Objectives: After completing this section, you should be able to do the following: Calculate the lengths of sides and angles of a right triangle using trigonometric

More information

3.0 Trigonometry Review

3.0 Trigonometry Review 3.0 Trigonometry Review In trigonometry problems, all vertices (corners or angles) of the triangle are labeled with capital letters. The right angle is usually labeled C. Sides are usually labeled with

More information

2.0 Trigonometry Review Date: Pythagorean Theorem: where c is always the.

2.0 Trigonometry Review Date: Pythagorean Theorem: where c is always the. 2.0 Trigonometry Review Date: Key Ideas: The three angles in a triangle sum to. Pythagorean Theorem: where c is always the. In trigonometry problems, all vertices (corners or angles) of the triangle are

More information

14.1 Similar Triangles and the Tangent Ratio Per Date Trigonometric Ratios Investigate the relationship of the tangent ratio.

14.1 Similar Triangles and the Tangent Ratio Per Date Trigonometric Ratios Investigate the relationship of the tangent ratio. 14.1 Similar Triangles and the Tangent Ratio Per Date Trigonometric Ratios Investigate the relationship of the tangent ratio. Using the space below, draw at least right triangles, each of which has one

More information

UNIT 5 TRIGONOMETRY Lesson 5.4: Calculating Sine, Cosine, and Tangent. Instruction. Guided Practice 5.4. Example 1

UNIT 5 TRIGONOMETRY Lesson 5.4: Calculating Sine, Cosine, and Tangent. Instruction. Guided Practice 5.4. Example 1 Lesson : Calculating Sine, Cosine, and Tangent Guided Practice Example 1 Leo is building a concrete pathway 150 feet long across a rectangular courtyard, as shown in the following figure. What is the length

More information

Lesson 10.1 TRIG RATIOS AND COMPLEMENTARY ANGLES PAGE 231

Lesson 10.1 TRIG RATIOS AND COMPLEMENTARY ANGLES PAGE 231 1 Lesson 10.1 TRIG RATIOS AND COMPLEMENTARY ANGLES PAGE 231 What is Trigonometry? 2 It is defined as the study of triangles and the relationships between their sides and the angles between these sides.

More information

Geometry- Unit 6 Notes. Simplifying Radicals

Geometry- Unit 6 Notes. Simplifying Radicals Geometry- Unit 6 Notes Name: Review: Evaluate the following WITHOUT a calculator. a) 2 2 b) 3 2 c) 4 2 d) 5 2 e) 6 2 f) 7 2 g) 8 2 h) 9 2 i) 10 2 j) 2 2 k) ( 2) 2 l) 2 0 Simplifying Radicals n r Example

More information

Adding vectors. Let s consider some vectors to be added.

Adding vectors. Let s consider some vectors to be added. Vectors Some physical quantities have both size and direction. These physical quantities are represented with vectors. A common example of a physical quantity that is represented with a vector is a force.

More information

PreCalculus Unit 1: Unit Circle Trig Quiz Review (Day 9)

PreCalculus Unit 1: Unit Circle Trig Quiz Review (Day 9) PreCalculus Unit 1: Unit Circle Trig Quiz Review (Day 9) Name Date Directions: You may NOT use Right Triangle Trigonometry for any of these problems! Use your unit circle knowledge to solve these problems.

More information

Review of Sine, Cosine, and Tangent for Right Triangle

Review of Sine, Cosine, and Tangent for Right Triangle Review of Sine, Cosine, and Tangent for Right Triangle In trigonometry problems, all vertices (corners or angles) of the triangle are labeled with capital letters. The right angle is usually labeled C.

More information

Chapter 2 Trigonometry

Chapter 2 Trigonometry Chapter 2 Trigonometry 1 Chapter 2 Trigonometry Angles in Standard Position Angles in Standard Position Any angle may be viewed as the rotation of a ray about its endpoint. The starting position of the

More information

Math 144 Activity #2 Right Triangle Trig and the Unit Circle

Math 144 Activity #2 Right Triangle Trig and the Unit Circle 1 p 1 Right Triangle Trigonometry Math 1 Activity #2 Right Triangle Trig and the Unit Circle We use right triangles to study trigonometry. In right triangles, we have found many relationships between the

More information

Student Instruction Sheet: Unit 4, Lesson 3. Primary Trigonometric Ratios

Student Instruction Sheet: Unit 4, Lesson 3. Primary Trigonometric Ratios Student Instruction Sheet: Unit 4, Lesson 3 Suggested Time: 75 minutes Primary Trigonometric Ratios What s important in this lesson: In this lesson, you will use trigonometry (sin, cos, tan) to measure

More information

Chapter 9: Right Triangle Trigonometry

Chapter 9: Right Triangle Trigonometry Haberman MTH 11 Section I: The Trigonometric Functions Chapter 9: Right Triangle Trigonometry As we studied in Intro to the Trigonometric Functions: Part 1, if we put the same angle in the center of two

More information

Ch. 2 Trigonometry Notes

Ch. 2 Trigonometry Notes First Name: Last Name: Block: Ch. Trigonometry Notes.0 PRE-REQUISITES: SOLVING RIGHT TRIANGLES.1 ANGLES IN STANDARD POSITION 6 Ch..1 HW: p. 83 #1,, 4, 5, 7, 9, 10, 8. - TRIGONOMETRIC FUNCTIONS OF AN ANGLE

More information

MAC Learning Objectives. Learning Objectives (Cont.) Module 2 Acute Angles and Right Triangles

MAC Learning Objectives. Learning Objectives (Cont.) Module 2 Acute Angles and Right Triangles MAC 1114 Module 2 Acute Angles and Right Triangles Learning Objectives Upon completing this module, you should be able to: 1. Express the trigonometric ratios in terms of the sides of the triangle given

More information

Trigonometry is concerned with the connection between the sides and angles in any right angled triangle.

Trigonometry is concerned with the connection between the sides and angles in any right angled triangle. Trigonometry Obj: I can to use trigonometry to find unknown sides and unknown angles in a triangle. Trigonometry is concerned with the connection between the sides and angles in any right angled triangle.

More information

Secondary Math 3- Honors. 7-4 Inverse Trigonometric Functions

Secondary Math 3- Honors. 7-4 Inverse Trigonometric Functions Secondary Math 3- Honors 7-4 Inverse Trigonometric Functions Warm Up Fill in the Unit What You Will Learn How to restrict the domain of trigonometric functions so that the inverse can be constructed. How

More information

7.1/7.2 Apply the Pythagorean Theorem and its Converse

7.1/7.2 Apply the Pythagorean Theorem and its Converse 7.1/7.2 Apply the Pythagorean Theorem and its Converse Remember what we know about a right triangle: In a right triangle, the square of the length of the is equal to the sum of the squares of the lengths

More information

1.6 Applying Trig Functions to Angles of Rotation

1.6 Applying Trig Functions to Angles of Rotation wwwck1org Chapter 1 Right Triangles and an Introduction to Trigonometry 16 Applying Trig Functions to Angles of Rotation Learning Objectives Find the values of the six trigonometric functions for angles

More information

1. Let be a point on the terminal side of θ. Find the 6 trig functions of θ. (Answers need not be rationalized). b. P 1,3. ( ) c. P 10, 6.

1. Let be a point on the terminal side of θ. Find the 6 trig functions of θ. (Answers need not be rationalized). b. P 1,3. ( ) c. P 10, 6. Q. Right Angle Trigonometry Trigonometry is an integral part of AP calculus. Students must know the basic trig function definitions in terms of opposite, adjacent and hypotenuse as well as the definitions

More information

Accel. Geometry - Concepts Similar Figures, Right Triangles, Trigonometry

Accel. Geometry - Concepts Similar Figures, Right Triangles, Trigonometry Accel. Geometry - Concepts 16-19 Similar Figures, Right Triangles, Trigonometry Concept 16 Ratios and Proportions (Section 7.1) Ratio: Proportion: Cross-Products Property If a b = c, then. d Properties

More information

Solv S ing olv ing ight ight riang les iangles 8-3 Solving Right Triangles Warm Up Use ABC for Exercises If a = 8 and b = 5, find c

Solv S ing olv ing ight ight riang les iangles 8-3 Solving Right Triangles Warm Up Use ABC for Exercises If a = 8 and b = 5, find c Warm Up Lesson Presentation Lesson Quiz Warm Up Use ABC for Exercises 1 3. 1. If a = 8 and b = 5, find c. 2. If a = 60 and c = 61, find b. 11 3. If b = 6 and c = 10, find sin B. 0.6 Find AB. 4. A(8, 10),

More information

UNIT 2 RIGHT TRIANGLE TRIGONOMETRY Lesson 2: Applying Trigonometric Ratios Instruction

UNIT 2 RIGHT TRIANGLE TRIGONOMETRY Lesson 2: Applying Trigonometric Ratios Instruction Prerequisite Skills This lesson requires the use of the following skills: manipulating the Pythagorean Theorem given any two sides of a right triangle defining the three basic trigonometric ratios (sine,

More information

(13) Page #1 8, 12, 13, 15, 16, Even, 29 32, 39 44

(13) Page #1 8, 12, 13, 15, 16, Even, 29 32, 39 44 Geometry/Trigonometry Unit 7: Right Triangle Notes Name: Date: Period: # (1) Page 430 #1 15 (2) Page 430 431 #16 23, 25 27, 29 and 31 (3) Page 437 438 #1 8, 9 19 odd (4) Page 437 439 #10 20 Even, 23, and

More information

Warm-Up Up Exercises. Use this diagram for Exercises If PR = 12 and m R = 19, find p. ANSWER If m P = 58 and r = 5, find p.

Warm-Up Up Exercises. Use this diagram for Exercises If PR = 12 and m R = 19, find p. ANSWER If m P = 58 and r = 5, find p. Warm-Up Up Exercises Use this diagram for Exercises 1 4. 1. If PR = 12 and m R = 19, find p. ANSWER 11.3 2. If m P = 58 and r = 5, find p. ANSWER 8.0 Warm-Up Up Exercises Use this diagram for Exercises

More information

Chapter 3: Right Triangle Trigonometry

Chapter 3: Right Triangle Trigonometry 10C Name: Chapter 3: Right Triangle Trigonometry 3.1 The Tangent Ratio Outcome : Develop and apply the tangent ratio to solve problems that involve right triangles. Definitions: Adjacent side: the side

More information

DAY 1 - GEOMETRY FLASHBACK

DAY 1 - GEOMETRY FLASHBACK DAY 1 - GEOMETRY FLASHBACK Sine Opposite Hypotenuse Cosine Adjacent Hypotenuse sin θ = opp. hyp. cos θ = adj. hyp. tan θ = opp. adj. Tangent Opposite Adjacent a 2 + b 2 = c 2 csc θ = hyp. opp. sec θ =

More information

9.1 Use Trigonometry with Right Triangles

9.1 Use Trigonometry with Right Triangles 9.1 Use Trigonometry with Right Triangles Use the Pythagorean Theorem to find missing lengths in right triangles. Find trigonometric ratios using right triangles. Use trigonometric ratios to find angle

More information

Common Core Standards Addressed in this Resource

Common Core Standards Addressed in this Resource Common Core Standards Addressed in this Resource N-CN.4 - Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and explain why the rectangular

More information

4.1: Angles & Angle Measure

4.1: Angles & Angle Measure 4.1: Angles & Angle Measure In Trigonometry, we use degrees to measure angles in triangles. However, degree is not user friendly in many situations (just as % is not user friendly unless we change it into

More information

Trigonometric Ratios and Functions

Trigonometric Ratios and Functions Algebra 2/Trig Unit 8 Notes Packet Name: Date: Period: # Trigonometric Ratios and Functions (1) Worksheet (Pythagorean Theorem and Special Right Triangles) (2) Worksheet (Special Right Triangles) (3) Page

More information

: Find the values of the six trigonometric functions for θ. Special Right Triangles:

: Find the values of the six trigonometric functions for θ. Special Right Triangles: ALGEBRA 2 CHAPTER 13 NOTES Section 13-1 Right Triangle Trig Understand and use trigonometric relationships of acute angles in triangles. 12.F.TF.3 CC.9- Determine side lengths of right triangles by using

More information

A trigonometric ratio is a,

A trigonometric ratio is a, ALGEBRA II Chapter 13 Notes The word trigonometry is derived from the ancient Greek language and means measurement of triangles. Section 13.1 Right-Triangle Trigonometry Objectives: 1. Find the trigonometric

More information

MATH EXAM 1 - SPRING 2018 SOLUTION

MATH EXAM 1 - SPRING 2018 SOLUTION MATH 140 - EXAM 1 - SPRING 018 SOLUTION 8 February 018 Instructor: Tom Cuchta Instructions: Show all work, clearly and in order, if you want to get full credit. If you claim something is true you must

More information

Summer Assignment for students entering: Algebra 2 Trigonometry Honors

Summer Assignment for students entering: Algebra 2 Trigonometry Honors Summer Assignment for students entering: Algebra Trigonometry Honors Please have the following worksheets completed and ready to be handed in on the first day of class in the fall. Make sure you show your

More information

Lesson Title 2: Problem TK Solving with Trigonometric Ratios

Lesson Title 2: Problem TK Solving with Trigonometric Ratios Part UNIT RIGHT solving TRIANGLE equations TRIGONOMETRY and inequalities Lesson Title : Problem TK Solving with Trigonometric Ratios Georgia Performance Standards MMG: Students will define and apply sine,

More information

Copyrighted by Gabriel Tang B.Ed., B.Sc. Page 167.

Copyrighted by Gabriel Tang B.Ed., B.Sc. Page 167. lgebra Chapter 8: nalytical Trigonometry 8- Inverse Trigonometric Functions Chapter 8: nalytical Trigonometry Inverse Trigonometric Function: - use when we are given a particular trigonometric ratio and

More information

UNIT 2 RIGHT TRIANGLE TRIGONOMETRY Lesson 1: Exploring Trigonometric Ratios Instruction

UNIT 2 RIGHT TRIANGLE TRIGONOMETRY Lesson 1: Exploring Trigonometric Ratios Instruction Prerequisite Skills This lesson requires the use of the following skills: measuring angles with a protractor understanding how to label angles and sides in triangles converting fractions into decimals

More information

MATHEMATICS FOR ENGINEERING TRIGONOMETRY

MATHEMATICS FOR ENGINEERING TRIGONOMETRY MATHEMATICS FOR ENGINEERING TRIGONOMETRY TUTORIAL SOME MORE RULES OF TRIGONOMETRY This is the one of a series of basic tutorials in mathematics aimed at beginners or anyone wanting to refresh themselves

More information

(Type your answer in radians. Round to the nearest hundredth as needed.)

(Type your answer in radians. Round to the nearest hundredth as needed.) 1. Find the exact value of the following expression within the interval (Simplify your answer. Type an exact answer, using as needed. Use integers or fractions for any numbers in the expression. Type N

More information

B. Dilate the following figure using a scale

B. Dilate the following figure using a scale 1 Dilations affect the size of the pre-image. he pre-image will enlarge or reduce by the ratio given by the scale factor. A dilation with a scale factor of k > 1 enlarges it. A dilation of 0 < k < 1 reduces

More information

Trigonometry Ratios. For each of the right triangles below, the labelled angle is equal to 40. Why then are these triangles similar to each other?

Trigonometry Ratios. For each of the right triangles below, the labelled angle is equal to 40. Why then are these triangles similar to each other? Name: Trigonometry Ratios A) An Activity with Similar Triangles Date: For each of the right triangles below, the labelled angle is equal to 40. Why then are these triangles similar to each other? Page

More information

Math for Geometric Optics

Math for Geometric Optics Algebra skills Math for Geometric Optics general rules some common types of equations units problems with several variables (substitution) Geometry basics Trigonometry Pythagorean theorem definitions,

More information

Ganado Unified School District Pre-Calculus 11 th /12 th Grade

Ganado Unified School District Pre-Calculus 11 th /12 th Grade Ganado Unified School District Pre-Calculus 11 th /12 th Grade PACING Guide SY 2016-2017 Timeline & Resources Quarter 1 AZ College and Career Readiness Standard HS.A-CED.4. Rearrange formulas to highlight

More information

Circular Trigonometry Notes April 24/25

Circular Trigonometry Notes April 24/25 Circular Trigonometry Notes April 24/25 First, let s review a little right triangle trigonometry: Imagine a right triangle with one side on the x-axis and one vertex at (0,0). We can write the sin(θ) and

More information

Student Instruction Sheet: Unit 4, Lesson 2. Ratios of Sides of Right-Angle Triangles

Student Instruction Sheet: Unit 4, Lesson 2. Ratios of Sides of Right-Angle Triangles Student Instruction Sheet: Unit 4, Lesson 2 Ratios of Sides of Right-Angle s Suggested Time: 75 minutes What s important in this lesson: In this lesson, you will learn through investigation, the relationship

More information

HW. Pg. 334 #1-9, 11, 12 WS. A/ Angles in Standard Position: Terminology: Initial Arm. Terminal Arm. Co-Terminal Angles. Quadrants

HW. Pg. 334 #1-9, 11, 12 WS. A/ Angles in Standard Position: Terminology: Initial Arm. Terminal Arm. Co-Terminal Angles. Quadrants MCR 3UI Introduction to Trig Functions Date: Lesson 6.1 A/ Angles in Standard Position: Terminology: Initial Arm HW. Pg. 334 #1-9, 11, 1 WS Terminal Arm Co-Terminal Angles Quadrants Related Acute Angles

More information

Sine (sin) = opposite hypotenuse

Sine (sin) = opposite hypotenuse ? Sine (sin) =? Sine (sin) = opposite hypotenuse ? Cosine (cos) =? Cosine (cos) = adjacent hypotenuse ? Tangent (tan) =? Tangent (tan) = opposite adjacent sin D=?? sin D = AB AD cos D=?? cos D = DB AD

More information

Ganado Unified School District Trigonometry/Pre-Calculus 12 th Grade

Ganado Unified School District Trigonometry/Pre-Calculus 12 th Grade Ganado Unified School District Trigonometry/Pre-Calculus 12 th Grade PACING Guide SY 2014-2015 Timeline & Resources Quarter 1 AZ College and Career Readiness Standard HS.A-CED.4. Rearrange formulas to

More information

Math 4 Snow Day. Name: Class: Date: Multiple Choice Identify the choice that best completes the statement or answers the question.

Math 4 Snow Day. Name: Class: Date: Multiple Choice Identify the choice that best completes the statement or answers the question. Class: Date: Math 4 Snow Day Multiple Choice Identify the choice that best completes the statement or answers the question.. Simplify the rational expression x x x x x x 0. x x. Which function has an amplitude

More information

UNIT 9 - RIGHT TRIANGLES AND TRIG FUNCTIONS

UNIT 9 - RIGHT TRIANGLES AND TRIG FUNCTIONS UNIT 9 - RIGHT TRIANGLES AND TRIG FUNCTIONS Converse of the Pythagorean Theorem Objectives: SWBAT use the converse of the Pythagorean Theorem to solve problems. SWBAT use side lengths to classify triangles

More information

Cumulative Review: SOHCAHTOA and Angles of Elevation and Depression

Cumulative Review: SOHCAHTOA and Angles of Elevation and Depression Cumulative Review: SOHCAHTOA and Angles of Elevation and Depression Part 1: Model Problems The purpose of this worksheet is to provide students the opportunity to review the following topics in right triangle

More information

Mathematics for Computer Graphics. Trigonometry

Mathematics for Computer Graphics. Trigonometry Mathematics for Computer Graphics Trigonometry Trigonometry...????? The word trigonometry is derived from the ancient Greek language and means measurement of triangles. trigonon triangle + metron measure

More information

Finding Angles and Solving Right Triangles NEW SKILLS: WORKING WITH INVERSE TRIGONOMETRIC RATIOS. Calculate each angle to the nearest degree.

Finding Angles and Solving Right Triangles NEW SKILLS: WORKING WITH INVERSE TRIGONOMETRIC RATIOS. Calculate each angle to the nearest degree. 324 MathWorks 10 Workbook 7.5 Finding Angles and Solving Right Triangles NEW SKILLS: WORKING WITH INVERSE TRIGONOMETRIC RATIOS The trigonometric ratios discussed in this chapter are unaffected by the size

More information

Study Guide and Review - Chapter 10

Study Guide and Review - Chapter 10 State whether each sentence is true or false. If false, replace the underlined word, phrase, expression, or number to make a true sentence. 1. A triangle with sides having measures of 3, 4, and 6 is a

More information

Right Triangle Trigonometry Definitions (Instructor Notes)

Right Triangle Trigonometry Definitions (Instructor Notes) Right Triangle Trigonometry Definitions (Instructor Notes) This activity is designed for a 50 min. class. Materials: Triangles Print out the last 10 pages of this document. It helps to use different colors

More information

Study Guide and Review - Chapter 10

Study Guide and Review - Chapter 10 State whether each sentence is true or false. If false, replace the underlined word, phrase, expression, or number to make a true sentence. 1. A triangle with sides having measures of 3, 4, and 6 is a

More information

SNAP Centre Workshop. Introduction to Trigonometry

SNAP Centre Workshop. Introduction to Trigonometry SNAP Centre Workshop Introduction to Trigonometry 62 Right Triangle Review A right triangle is any triangle that contains a 90 degree angle. There are six pieces of information we can know about a given

More information

Angles of a Triangle. Activity: Show proof that the sum of the angles of a triangle add up to Finding the third angle of a triangle

Angles of a Triangle. Activity: Show proof that the sum of the angles of a triangle add up to Finding the third angle of a triangle Angles of a Triangle Activity: Show proof that the sum of the angles of a triangle add up to 180 0 Finding the third angle of a triangle Pythagorean Theorem Is defined as the square of the length of the

More information

A lg e b ra II. Trig o n o m e tric F u n c tio

A lg e b ra II. Trig o n o m e tric F u n c tio 1 A lg e b ra II Trig o n o m e tric F u n c tio 2015-12-17 www.njctl.org 2 Trig Functions click on the topic to go to that section Radians & Degrees & Co-terminal angles Arc Length & Area of a Sector

More information

Worksheet #1 Fractions

Worksheet #1 Fractions Worksheet # Fractions " Evaluate each expression and leave your answer in simplest form. ] 7 ] = ] + 8 ] + ] 7 ] 7 8 + 7] 7 8] 8 9] 8 0] 9 0 ] ] 9 ] 0 #" Worksheet # Simplifying/Evaluating Expressions

More information

hypotenuse adjacent leg Preliminary Information: SOH CAH TOA is an acronym to represent the following three 28 m 28 m opposite leg 13 m

hypotenuse adjacent leg Preliminary Information: SOH CAH TOA is an acronym to represent the following three 28 m 28 m opposite leg 13 m On Twitter: twitter.com/engagingmath On FaceBook: www.mathworksheetsgo.com/facebook I. odel Problems II. Practice Problems III. Challenge Problems IV. Answer ey Web Resources Using the inverse sine, cosine,

More information

Ganado Unified School District #20 (Pre-Calculus 11th/12th Grade)

Ganado Unified School District #20 (Pre-Calculus 11th/12th Grade) Ganado Unified School District #20 (Pre-Calculus 11th/12th Grade) PACING Guide SY 2018-2019 Timeline & Quarter 1 AZ College and Career Readiness Standard HS.A-CED.4. Rearrange formulas to highlight a quantity

More information

Right Triangle Trigonometry

Right Triangle Trigonometry Right Triangle Trigonometry 1 The six trigonometric functions of a right triangle, with an acute angle, are defined by ratios of two sides of the triangle. hyp opp The sides of the right triangle are:

More information

Trigonometry Summer Assignment

Trigonometry Summer Assignment Name: Trigonometry Summer Assignment Due Date: The beginning of class on September 8, 017. The purpose of this assignment is to have you practice the mathematical skills necessary to be successful in Trigonometry.

More information

Name: Unit 8 Right Triangles and Trigonometry Unit 8 Similarity and Trigonometry. Date Target Assignment Done!

Name: Unit 8 Right Triangles and Trigonometry Unit 8 Similarity and Trigonometry. Date Target Assignment Done! Unit 8 Similarity and Trigonometry Date Target Assignment Done! M 1-22 8.1a 8.1a Worksheet T 1-23 8.1b 8.1b Worksheet W 1-24 8.2a 8.2a Worksheet R 1-25 8.2b 8.2b Worksheet F 1-26 Quiz Quiz 8.1-8.2 M 1-29

More information

4-6 Inverse Trigonometric Functions

4-6 Inverse Trigonometric Functions Find the exact value of each expression, if it exists. 29. The inverse property applies, because lies on the interval [ 1, 1]. Therefore, =. 31. The inverse property applies, because lies on the interval

More information

Find the value of x. Then find the value of sin θ, cos θ, and tan θ for the triangle. 1.

Find the value of x. Then find the value of sin θ, cos θ, and tan θ for the triangle. 1. 9.6 Warmup Find the value of x. Then find the value of sin θ, cos θ, and tan θ for the triangle. 1. Find the value of the unknown sides. 2.. March 30, 2017 Geometry 9.6 Solving Right Triangles 1 Geometry

More information

Unit O Student Success Sheet (SSS) Right Triangle Trigonometry (sections 4.3, 4.8)

Unit O Student Success Sheet (SSS) Right Triangle Trigonometry (sections 4.3, 4.8) Unit O Student Success Sheet (SSS) Right Triangle Trigonometry (sections 4.3, 4.8) Standards: Geom 19.0, Geom 20.0, Trig 7.0, Trig 8.0, Trig 12.0 Segerstrom High School -- Math Analysis Honors Name: Period:

More information

Algebra II. Slide 1 / 162. Slide 2 / 162. Slide 3 / 162. Trigonometric Functions. Trig Functions

Algebra II. Slide 1 / 162. Slide 2 / 162. Slide 3 / 162. Trigonometric Functions. Trig Functions Slide 1 / 162 Algebra II Slide 2 / 162 Trigonometric Functions 2015-12-17 www.njctl.org Trig Functions click on the topic to go to that section Slide 3 / 162 Radians & Degrees & Co-terminal angles Arc

More information

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Precalculus CP Final Exam Review - 01 Name Date: / / MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Convert the angle in degrees to radians. Express

More information

This unit is built upon your knowledge and understanding of the right triangle trigonometric ratios. A memory aid that is often used was SOHCAHTOA.

This unit is built upon your knowledge and understanding of the right triangle trigonometric ratios. A memory aid that is often used was SOHCAHTOA. Angular Rotations This unit is built upon your knowledge and understanding of the right triangle trigonometric ratios. A memory aid that is often used was SOHCAHTOA. sin x = opposite hypotenuse cosx =

More information

Chapter 7. Right Triangles and Trigonometry

Chapter 7. Right Triangles and Trigonometry hapter 7 Right Triangles and Trigonometry 7.1 pply the Pythagorean Theorem 7.2 Use the onverse of the Pythagorean Theorem 7.3 Use Similar Right Triangles 7.4 Special Right Triangles 7.5 pply the Tangent

More information

to and go find the only place where the tangent of that

to and go find the only place where the tangent of that Study Guide for PART II of the Spring 14 MAT187 Final Exam. NO CALCULATORS are permitted on this part of the Final Exam. This part of the Final exam will consist of 5 multiple choice questions. You will

More information

Ch 8: Right Triangles and Trigonometry 8-1 The Pythagorean Theorem and Its Converse 8-2 Special Right Triangles 8-3 The Tangent Ratio

Ch 8: Right Triangles and Trigonometry 8-1 The Pythagorean Theorem and Its Converse 8-2 Special Right Triangles 8-3 The Tangent Ratio Ch 8: Right Triangles and Trigonometry 8-1 The Pythagorean Theorem and Its Converse 8- Special Right Triangles 8-3 The Tangent Ratio 8-1: The Pythagorean Theorem and Its Converse Focused Learning Target:

More information

Section 4.1: Introduction to Trigonometry

Section 4.1: Introduction to Trigonometry Section 4.1: Introduction to Trigonometry Review of Triangles Recall that the sum of all angles in any triangle is 180. Let s look at what this means for a right triangle: A right angle is an angle which

More information

CLEP Pre-Calculus. Section 1: Time 30 Minutes 50 Questions. 1. According to the tables for f(x) and g(x) below, what is the value of [f + g]( 1)?

CLEP Pre-Calculus. Section 1: Time 30 Minutes 50 Questions. 1. According to the tables for f(x) and g(x) below, what is the value of [f + g]( 1)? CLEP Pre-Calculus Section : Time 0 Minutes 50 Questions For each question below, choose the best answer from the choices given. An online graphing calculator (non-cas) is allowed to be used for this section..

More information

Pythagoras Theorem. Recall. Pythagoras theorem gives the relationship between the lengths of side in right angled triangles.

Pythagoras Theorem. Recall. Pythagoras theorem gives the relationship between the lengths of side in right angled triangles. Pythagoras Theorem Recall Pythagoras theorem gives the relationship between the lengths of side in right angled triangles. It is generally conveyed as follows: The square of the hypotenuse is equal to

More information

Algebra II. Slide 1 / 92. Slide 2 / 92. Slide 3 / 92. Trigonometry of the Triangle. Trig Functions

Algebra II. Slide 1 / 92. Slide 2 / 92. Slide 3 / 92. Trigonometry of the Triangle. Trig Functions Slide 1 / 92 Algebra II Slide 2 / 92 Trigonometry of the Triangle 2015-04-21 www.njctl.org Trig Functions click on the topic to go to that section Slide 3 / 92 Trigonometry of the Right Triangle Inverse

More information

Name: Block: What I can do for this unit:

Name: Block: What I can do for this unit: Unit 8: Trigonometry Student Tracking Sheet Math 10 Common Name: Block: What I can do for this unit: After Practice After Review How I Did 8-1 I can use and understand triangle similarity and the Pythagorean

More information

architecture, physics... you name it, they probably use it.

architecture, physics... you name it, they probably use it. The Cosine Ratio Cosine Ratio, Secant Ratio, and Inverse Cosine.4 Learning Goals In this lesson, you will: Use the cosine ratio in a right triangle to solve for unknown side lengths. Use the secant ratio

More information

and how to label right triangles:

and how to label right triangles: Grade 9 IGCSE A1: Chapter 6 Trigonometry Items you need at some point in the unit of study: Graph Paper Exercise 2&3: Solving Right Triangles using Trigonometry Trigonometry is a branch of mathematics

More information

A lg e b ra II. Trig o n o m e try o f th e Tria n g le

A lg e b ra II. Trig o n o m e try o f th e Tria n g le 1 A lg e b ra II Trig o n o m e try o f th e Tria n g le 2015-04-21 www.njctl.org 2 Trig Functions click on the topic to go to that section Trigonometry of the Right Triangle Inverse Trig Functions Problem

More information

Sec 4.1 Trigonometric Identities Basic Identities. Name: Reciprocal Identities:

Sec 4.1 Trigonometric Identities Basic Identities. Name: Reciprocal Identities: Sec 4. Trigonometric Identities Basic Identities Name: Reciprocal Identities: Quotient Identities: sin csc cos sec csc sin sec cos sin tan cos cos cot sin tan cot cot tan Using the Reciprocal and Quotient

More information

Lesson 5.6: Angles in Standard Position

Lesson 5.6: Angles in Standard Position Lesson 5.6: Angles in Standard Position IM3 - Santowski IM3 - Santowski 1 Fast Five Opening Exercises! Use your TI 84 calculator:! Evaluate sin(50 ) " illustrate with a diagram! Evaluate sin(130 ) " Q

More information

8-1 Simple Trigonometric Equations. Objective: To solve simple Trigonometric Equations and apply them

8-1 Simple Trigonometric Equations. Objective: To solve simple Trigonometric Equations and apply them Warm Up Use your knowledge of UC to find at least one value for q. 1) sin θ = 1 2 2) cos θ = 3 2 3) tan θ = 1 State as many angles as you can that are referenced by each: 1) 30 2) π 3 3) 0.65 radians Useful

More information

Algebra II Trigonometric Functions

Algebra II Trigonometric Functions Slide 1 / 162 Slide 2 / 162 Algebra II Trigonometric Functions 2015-12-17 www.njctl.org Slide 3 / 162 Trig Functions click on the topic to go to that section Radians & Degrees & Co-terminal angles Arc

More information

Section 14: Trigonometry Part 1

Section 14: Trigonometry Part 1 Section 14: Trigonometry Part 1 The following Mathematics Florida Standards will be covered in this section: MAFS.912.F-TF.1.1 MAFS.912.F-TF.1.2 MAFS.912.F-TF.1.3 Understand radian measure of an angle

More information

Trig/Math Anal Name No HW NO. SECTIONS ASSIGNMENT DUE TG 1. Practice Set J #1, 9*, 13, 17, 21, 22

Trig/Math Anal Name No HW NO. SECTIONS ASSIGNMENT DUE TG 1. Practice Set J #1, 9*, 13, 17, 21, 22 Trig/Math Anal Name No LATE AND ABSENT HOMEWORK IS ACCEPTED UP TO THE TIME OF THE CHAPTER TEST ON NO GRAPHING CALCULATORS ALLOWED ON THIS TEST HW NO. SECTIONS ASSIGNMENT DUE TG (per & amp) Practice Set

More information

Geometry SIA #3. Name: Class: Date: Short Answer. 1. Find the perimeter of parallelogram ABCD with vertices A( 2, 2), B(4, 2), C( 6, 1), and D(0, 1).

Geometry SIA #3. Name: Class: Date: Short Answer. 1. Find the perimeter of parallelogram ABCD with vertices A( 2, 2), B(4, 2), C( 6, 1), and D(0, 1). Name: Class: Date: ID: A Geometry SIA #3 Short Answer 1. Find the perimeter of parallelogram ABCD with vertices A( 2, 2), B(4, 2), C( 6, 1), and D(0, 1). 2. If the perimeter of a square is 72 inches, what

More information

ACT Math test Trigonometry Review

ACT Math test Trigonometry Review Many students are a little scared of trig, but the ACT seems to overcompensate for that fact by testing trig in an extremely straightforward way. ACT trig is basically all about right triangles. When it

More information

Packet Unit 5 Trigonometry Honors Math 2 17

Packet Unit 5 Trigonometry Honors Math 2 17 Packet Unit 5 Trigonometry Honors Math 2 17 Homework Day 12 Part 1 Cumulative Review of this unit Show ALL work for the following problems! Use separate paper, if needed. 1) If AC = 34, AB = 16, find sin

More information

1. The circle below is referred to as a unit circle. Why is this the circle s name?

1. The circle below is referred to as a unit circle. Why is this the circle s name? Right Triangles and Coordinates on the Unit Circle Learning Task: 1. The circle below is referred to as a unit circle. Why is this the circle s name? Part I 2. Using a protractor, measure a 30 o angle

More information

Study Guide and Review

Study Guide and Review Choose the term that best matches the statement or phrase. a square of a whole number A perfect square is a square of a whole number. a triangle with no congruent sides A scalene triangle has no congruent

More information

Three Angle Measure. Introduction to Trigonometry. LESSON 9.1 Assignment

Three Angle Measure. Introduction to Trigonometry. LESSON 9.1 Assignment LESSON.1 Assignment Name Date Three Angle Measure Introduction to Trigonometry 1. Analyze triangle A and triangle DEF. Use /A and /D as the reference angles. E 7.0 cm 10.5 cm A 35 10.0 cm D 35 15.0 cm

More information

Be sure to label all answers and leave answers in exact simplified form.

Be sure to label all answers and leave answers in exact simplified form. Pythagorean Theorem word problems Solve each of the following. Please draw a picture and use the Pythagorean Theorem to solve. Be sure to label all answers and leave answers in exact simplified form. 1.

More information

2) In a right triangle, with acute angle θ, sin θ = 7/9. What is the value of tan θ?

2) In a right triangle, with acute angle θ, sin θ = 7/9. What is the value of tan θ? CC Geometry H Aim #26: Students rewrite the Pythagorean theorem in terms of sine and cosine ratios and write tangent as an identity in terms of sine and cosine. Do Now: 1) In a right triangle, with acute

More information

Unit 6 Introduction to Trigonometry

Unit 6 Introduction to Trigonometry Lesson 1: Incredibly Useful Ratios Opening Exercise Unit 6 Introduction to Trigonometry Use right triangle ΔABC to answer 1 3. 1. Name the side of the triangle opposite A in two different ways. 2. Name

More information