MAP4CI Date Lesson Text Assigned Work Done Ref. Pythagorean Theorem, Pg 72 # 4-7, 9,10 ab P9 93 # 3, 6, 10, 11, 12

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1 MAP4CI Name: Trigonometry Unit 2 Outline Reminder: Write a missed Quiz or Test in room 540 at lunch or on your spare on the first day of return to school. If you have any concerns, please see Mrs. Behnke ASAP Date Lesson Text Assigned Work Done Ref. Pythagorean Theorem, Pg 72 # 4-7, 9,10 ab Day 1: Tues. Oct.20 Trig Intro Day 2: Wed. Oct. 21 Solving Equations, Primary Trig Ratios Day 3: Thur. Oct22 Determining Lengths of Sides in Right 2.1 Pg 80 # la, 2a, 3,4, 9, 10, 12 Day 4: Fri. Oct. 23 Triangles Day 1: Mon. Oct.26 Determining Measures of Angles in 2.1 Pg 80 # 5, 6, 7, 11, 13 Day 2: Tues. Oct. 27 Right Triangles Day 3: Wed. Oct. 28 The Trigonometric Ratios of Obtuse 2.2 Worksheet Day 4: Thurs. Angles - Oct. Part Day 1: Fri. Oct. 30 The Trig Ratios of Obtuse Angles Day 2: Mon. Nov. 2 Part 2 Day 3: Tues. Nov. 3 Review Day 4: Wed. Nov. 4 QUIZ P9 93 # 3, 6, 10, 11, 12 Day 1: Thurs. Nov. 5 Sine Law 2.3 Pg 101 # 1a, 2, 4a, 6, 7a, 8 Day 2: Fri. Nov. 6 Day 3: Mon. Nov. 9 Applications Involving Sine Law 2.3 Pg 102 # 9, 10, 11, 14 Day 4: Tues. Nov. 10 Day 1: Wed. Nov. 11 cosine Law 2.4 Pg 110 # 1 a, 3, 4a, 5, 6, 7a Day 2: Thurs. Nov. 12 Fri. Nov. 13 PD DAY Day 3: Mon. Nov.16 Applications Involving Cosine Law 2.4 Pg 110 # 7b, 9, 10, 11, 12 Day 4: Tues. Nov. 17 Day 1: Wed. Nov.18 Applications of Trigonometry 2.5 Pg 126 # 1, 2, 3, 5, 7, 9, 11 Day 2: Thurs. Nov. 19 Day 3: Fri. Nov. 20 Review (Practice Test) Pg 132 # 1-12 Day 4: Mon. Nov.23 Day 1: Tues. Nov. 24 Unit Two Test Day 2: Wed. Nov. 25

2 becidina how to solve a trianale? Formula Picture When to use Pythagorean Trig Ratios Sine Law Cosine Law

3 J-k MAP 4C1 Trigonometry Intro Date: **set your calculator to begree mode 1. Pythagorean Theorem. Draw a right triangle. Label the sides a, b and c (c must be the longest side). Side c is called the Now draw a square on each side of the triangle. State the relationship between the squares on the sides of the right triangle. Ex. 1 Determine the length of the indicated side. 0.5 cm Ex. 2 Brad walks 1.7 km North and then 1.5 km East along the sides of a park. ban starts at the same point and takes a shortcut along the diagonal. How much shorter is bans walk? 2. Solving Equations. Ex. 1 Solve for x to the nearest tenth.

4 tangent 9 Practice: Pg 72 # 4-7, c) tan6l = To remember the 3 primary a) sin54= cosine 9 z sine 9 z The 3 primary trig ratios are: relative to angle e use 9, 10 ab Check Answers: Pg. 540 b) cosl4= Ex. 2 Evaluate to four decimal places. Ex. 1 Write the 3 primary trig ratios relative to trig, ratios of the sides of a right triangle sides hypotenuse, side opposite to angle e, and side adjacent to angle Primary Trig Ratios. Given a right triangle with angle 9 (theta), label the

5 \Jr% \essn Determining Measures of Angles in Right Triang[ Trig ratios can also be used to find the measures of angles of a right triangle that are not known. Examøles: For the following triangles identify the trig ratio to use, write the equation and solve it to one decimal place using the inverse trig buttons r&i1 I I H I on yqur calculator. a) N Have: H Need: 12 Use: b)zie: c) Have: Need: Use: Lx. 2 Solve XYZ given that LX = 90, x = 8.2cm, z = 6.0cm. To solve means Practice Assignment: Pg. 80 #5,6,7, 11, 13 V Answers Pg

6 Unit 2 Lesson 4: Investigating Obtuse Angles Introduction to the Activity: In this activity, you will use your calculator and the following chart to investigate the trigonometric ratios of obtuse angles. Then, you will analyze the results to determine any patterns. Performing the Activity 1) Refer to the chart that follows. For each of the listed angles, use your calculator to determine the value of each primary trigonometric ratio in the chart. 2) After you have completed the chart, answer the questions that follow. I Round values to 3 decimal places. There will be some rounding error. Primary Angle, B sin B cos B tan B hyp hyp adj

7 Investigating Obtuse Angles (Continued) After you have completed the chart, answer the following questions. 1) What do you notice about the signs (positive? negative?) of the values of sin B? Be as specific as possible. Why does this happen? 2) What do you notice about the signs (positive? negative?) of the values of cos B? Be as specific as possible. Why does this happen? 3) What do you notice about the signs (positive? negative?) of the values of tan B? Be as specific as possible. Why does this happen? 4) Write down pairs of LB that have approximately the same value for sin B. Verify that the values are actually the same using your calculator For example, check that sin 5 and sin 175 give the same value. How are the angles related to each other? Using the same pairs of angles, what do you notice about the values of cos B? (Verify on your calculator if needed.) Using the same pairs of angles, what do you notice about the values of tan B? (Verify on your calculator if needed.) 5) Use sin1 on your calculator to solve for angle B in sin B = 0.5. What value does your calculator give? What other value for B is possible? How can you quickly determine the value of the second angle? Complete the following using a calculator and what you have learned: sinbo.7660 B= or B sin B = or B =

8 a) Sketch a diagram for this angle in standard position. through A(2, 4). 1. The terminal arm of an angle. 9, in standard position passes Praotiae Obtuse Angles [2.2J Trigonometric Ratios With Jfl14 a. L_e3SonL4 rar4-a ) I jlq 60 Anglt;. Sine:. J Cnsiné;: positive or negative. Round your answers to three decimal places. 3. Complete the table. For each angle, indicate whether each trigonometric ratio is c) Determinethe primary trigonometric ratios to three decimal places. b) Determine the length of 08. ft 3 LET: LTH ut ttfti:lri a) Sketch a diagram for this angle in standard position. 2. The terminal arm of an angle, 9. in standard position passes through B( 5, 6). c) Determine the primary trigonometric ratios to three decimal places. b) Determine the length of OA.

9 MAP 4C1 Trigonometric Ratios for Obtuse Angles in Standard Position Unit 2 Lesson 5 Date: 1. The sine of an obtuse angle, 8, in standard position is - a) Identify the coordinates of a point that lies on the terminal arm of /3. b) Sketch a diagram of /3 I fl 6*::, 6I**H *1 :.! c) Determine cos 8 and tan 8. d) Determine the measure of /3, using a calculator. 2. The tangent of an obtuse angle, 8, in standard position is 1 a) Identify the coordinates of a point b) Sketch a diagram of /3. that lies on the terminal arm of /3. y. In. 4 a.!. Ifl c) Determine sin 8 and cos 0. Round your answers to three decimal places. d) Determine the measure of using a calculator. /49,

10 MAP4CI Unit 2 lesson 7 APPLICATIONS OF SINE LAW 1. Two people stand approximately 50 m apart on level ground. One person measures the angle of elevation of a hot air balloon to be 58. The other person measures the angle of elevation to be 41. How far is each person from the hot air balloon?

11 Direction Unit 2 Lesson 9: Cosine Law Applications Review Cosine Law: The Cosine Law can be used to solve for an unknown side, if you are given two sides and a contained angle: a2=b2+c2-2 bccosa It can also be re-arranged to solve for an unknown angle: cosa = + 2bc a2 Bearings: Direction can be written in several ways Direction bearing Diagram N60 E Diagram Bearing - Diagram Bearing Direction Wi V P P S 600 S N Provide a sketch here. Wi 235 P S

12 MAP 4C1 Unit 2 Lesson 10 Applications of Trigonometry Date: Lx. 1 From the top of a vertical cliff a person measures the angle of depression of a boat as 9. The height of the cliff is 142 m. How far is the boat from the base of the cliff? Round your answer to the nearest m. Lx. 2 Find the length of TU to the nearest tenth. R U S 8cm T Ex. 3 A smokestack, AB, is 205m high. From two points C and Don the same side of the smokestack s base B, the angles of elevation to the top of the smokestack are 40 and 36 respectively. Find the distance between C and D to the nearest metre. A 205 m B C D Lx. 4 Two guy-wires are anchored at the same point. The first guy-wire is 12 m in length and is attached to the top of a tower. The second guy-wire is 9 m in length and is attached to a point 5 m below the top of the tower. How far are the wires anchored from the base of the tower? Round your answer to the nearest tenth of a metre. Practice Assignment: Pg 126 # 1,2, 3, 5, 7, 9, 11 V Answers Pg

13 Unit 2 Lesson 11 part 1: Review FOR RIGHT ANGLE TRIANGLES PYTHGOREAN Formula a2 + b2 = c2 where c must be the hypotenuse SOHCA HTOA opp cuff opp sin9=,cos(8)=r,tan(8)= hyp hyp adj FOR OBLIQUE TRIANGLES (non-right angled, including obtuse triangles) Sine Law sina sinb sinc a c = = or = = a b c sina sins sinc Use when you have 2 sides and one opposite angle 2 angles and one opposite side a2 = b2 + c2 2bccosA Cosine Law or cosa = Use when you have 2 sides and a contained angle (find the opposite side) b2 +c2 a2 2 bc All three sides (find an angle)

14 1. A harbour master uses radar to monitor two ships. B and C, as they approach the harbour, H. One ship is 5.3 miles from the harbour on a bearing of 032. The other ship is 7.4 miles away from the harbour on a bearing of 295. How far apart are the two ships? 2. An aircraft navigator knows that town A is 71 km due north of the airport town B is 201 km from the airport, and towns A and B are 241 km apart. On what bearing should she plan the course from the airport to town B?

15 Obtuse Angles Obtuse angle e 1800 Supplementary Angles A+B=180 sina =sinb, coca = -cosb, tctna = -tenth The primary trigonometric ratios of an angle, in standard position are defined in terms of the coordinates of a point, (x, y), on the terminal arm, as follows: sine=! cosb=! tan6=1 where r=jx2 +y2 Bearing and Directions Bearings - 050, Directions N50 E N E65S 155 w E Types of Problems Directions, Solve a Triangle Area S Practice Drawing Triangles. Draw the following triangles, state unknowns and approach to solving: 1. Triangle ABC, where a=3m, b=4m, A=90 2. Triangle XYZ, where X=108, z=27mm, y=l2mm. 3. Triangle PUR, where P=43, R=118, q=som.

16 Example #1 : Calculate the length of the unknown side in each triangle. a. b. c. A M 3.0cm 3.Om 3.0cm e B 4.0cm C V z L N Example #2 : Calculate the indicated angle in each triangle. a. b. C. A x Z M 5.5cm 3Mm 5.Om 120m B 4.0cm C L 145 m N Example #3 A boat is proceeding on a bearing of 045 at 12 km/hr. At 3:00PM the captain sees a navigation buoy at 020. He sights the same buoy at 230 at 4:15. How many km s is the boat from the buoy at 4:15PM? a. Draw the figure b. Determine what Trig Ru$es to use c. Solve for unknown.

17 Deciding how to solve a triangle? Formula Picture When to use Pythagorean Right angle triangle a = b2 +c2 a - given 2 sides - asked to find third side Trig Ratios SOHCAHTOA B A b Sine Law B a b c sina sinb sinc Cosine Law C b Right angle triangle - two sides - given - given one side and - asked to find angle an angle side No right angle - given two angles - asked asked to find to find and one opposite other opposite = side side A given - given two sides - asked to find b and one opposite other opposite B angle angle No right angle two sides c& a - calculate the a =b +c 2becosA contained angle third side :os A = b2 + a2 A - given three sides - 2bc b angle can calculate