Trigonometry Summer Assignment

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1 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. All of the skills covered in this packet are from Geometry, Algebra 1, and Algebra. The material covered is from our district approved, Pearson Common Core, textbooks. If you need to, you may use reference materials to refresh your memory (old notes, textbooks, online resources, etc.). While graphing calculators will be used during a few tests and quizzes, the majority of in class assessments are non-calculator. You are encouraged to learn how to be calculator-independent. At the end of this page, there are links to some suggested online calculators. Trigonometry is a fast paced course that is taught at the college level to prepare you for college work. There is a lot of material in the curriculum that must be covered before the end of the year. Therefore, we cannot spend a lot of class time re-teaching prerequisite skills. This is why you have this packet. Spend some time with it and make sure you are clear on everything covered in this packet so that you will be successful in Trigonometry. Of course, you are always welcomed to seek help from your teacher if necessary. This assignment will be collected and graded as your first test, the last class day of the first week of school. Be sure to show all appropriate work to support your answers. In addition, there may be a quiz on this material during the first quarter. All questions must be complete with the correct work. You must return in September knowing how to do all the material in this packet. For assistance with the packet you may contact me at gnaem@roselleschools.org. s may take a few days during summer for a response. Please be specific in your for what you need assistance with, include the section and the question number as well. For each question in the packet, there is an example in the separate tutorial packet. The tutorial packet is posted online on our school s website. Reference to page and example numbers is listed under each question. Calculators Links Online Calculator Emulator for Download Good Luck! MATHACHS TRIGONOMETRY SUMMER ASSIGNMENT JUNE, 017 Page 1

2 1) Solve the following proportions. (Tutorial Page Example #1 & ) a) About 45 of every 300 apples picked at the Newbury Apple Orchard are rotten. If 3560 apples were picked one week, about how many apples were rotten? b) The ratio of the two acute angles in a right triangle is 5 : 13. What is the measure of each angle in the right triangle? ) Use Pythagorean Theorem to solve. (Tutorial Page 3 Example #1 & ) a) Right ABC has legs of lengths 4 ft and 7 ft. What is the length of the triangle s hypotenuse? b) Classify the triangle with sides 7, 9, and10 as acute, right, or obtuse. 3) Use the diagrams below each exercise to complete a b. (Tutorial Page 4 Example #1 & ) a) Find the length of the leg of the triangle. b) Find the length of the hypotenuse, g, of the triangle. MATHACHS TRIGONOMETRY SUMMER ASSIGNMENT JUNE, 017 Page

3 4) Solve the following. (Tutorial Page 5 Example #1 & ) a) Find the value of t to the nearest tenth. b) Find m M to the nearest degree. 5) Find the value of x. Round the lengths to the nearest tenth of a unit. (Tutorial Page 6 Example #1 & ) a) b) MATHACHS TRIGONOMETRY SUMMER ASSIGNMENT JUNE, 017 Page 3

4 6) Use vectors to answer the following. (Tutorial Page 7 Example #1 & ) a) Describe the direction of each vector. b) Find the magnitude of the given vector to the nearest tenth. 7) Find the area of each geometric shape. (Tutorial Page 8 Example #1 & ) a) b) c) MATHACHS TRIGONOMETRY SUMMER ASSIGNMENT JUNE, 017 Page 4

5 8) Write the standard equation of the circle from the given information. (Tutorial Page 9 Example #1 & ) a) Center (, 4); Point (6, 4) b) 9) Answer the following: (Tutorial Page 10 Example #1 & ) a) Find the circumference of the circle. Leave your answers in terms of π. b) Find the length of arc UV!. Leave your answers in terms of π. 10) Find the areas of circles and sectors described below. Write your answer in terms of π and round to the nearest tenth. (Tutorial Page 11 Example #1 & ) a) Circle with radius 5. b) Sector ABC in circle B of radius 4 and mac!. MATHACHS TRIGONOMETRY SUMMER ASSIGNMENT JUNE, 017 Page 5

6 11) Solve each equation for the indicated variable. (Tutorial Page 1 Example #1) a) f + 5 g = 1 fg,for f b) 3 1 a 3y + 4 = a+ y, for y b c) x + k 3 1 =, for x d) j 4 r + 3s = 1, for r 1) Solve each inequality. Graph the solution. (Tutorial Page 13 Example #1 & ) a) 4 (x 4) 5 (4x + 3) b) 7 7(x 7) > 4 + 5x MATHACHS TRIGONOMETRY SUMMER ASSIGNMENT JUNE, 017 Page 6

7 13) Solve each absolute value equation. Check your work. (Tutorial Page 14 Example #1) a) x 3 4 = 3 b) 3x = 13 x 14) Complete the steps to solve the inequality 4 3. (Tutorial Page 14 Example #) x a) 4 Rewrite as a compound inequality. x b) Add to each part. c) x Multiply each part by. d) What is the solution? 15) Evaluate each function for the given value of x, and write the input and the output as an ordered pair. (Tutorial Page 7 Example #3) a) h(x) = 1x for x = 4 b) t(x) = 8x 5 for x = 7 MATHACHS TRIGONOMETRY SUMMER ASSIGNMENT JUNE, 017 Page 7

8 16) Write an equation for each line. (Tutorial Page 15 Example #1) a) m = 4; contains (3, ) b) m = 1; contains (0, 7) c) d) 17) Graph each equation. (Tutorial Page 15 Example #) a) 3x + y = 6 b) 3y + x = 3 c) y 6 = 0 d) x + 4y 3 = 0 MATHACHS TRIGONOMETRY SUMMER ASSIGNMENT JUNE, 017 Page 8

9 18) Using point-slope form, write an equation of the line through each pair of points. (Tutorial Page 16 Example #1) a) (, 5) and (8, 3) b) (3, 5) and (0, 7) 19) Write an equation of each line in slope-intercept form. (Tutorial Page 16 Example # & 3) a) Through (, ) and parallel to y = 5x 4 b) Through ( 4, 1) and perpendicular to y = 3x + 7 MATHACHS TRIGONOMETRY SUMMER ASSIGNMENT JUNE, 017 Page 9

10 0) Solve each system by graphing or using a table. Check your answers. (Tutorial Page 17 Example #1) x + y + 3= 0 x + y = a) b) x 1 = y x + 3 y = 3 1) Solve each system. (Tutorial Page 18 Example #1 & ) a) Solve each system by substitution. m + n = 6 7 m + 6 n = 1 b) Solve each system by elimination. 5 f + 4 m = 6 f 3 m = 1 MATHACHS TRIGONOMETRY SUMMER ASSIGNMENT JUNE, 017 Page 10

11 ) Factor each expression. (Tutorial Page 19 Example #1 & ) a) x + 6x + 8 b) x 6x + 4 c) 9x 6x + 1 d) 3x + x 8 e) 7x 1 f) 16x 3x + 16 g) x 64 h) 15x 100x + 0 MATHACHS TRIGONOMETRY SUMMER ASSIGNMENT JUNE, 017 Page 11

12 3) Solve each equation by factoring. Check your answers. (Tutorial Page 0 Example #1) a) x 10x + 16 = 0 b) x = 5x + 1 c) x + 10x = 0 d) 3x 5x + = 0 4) What value completes the square for each expression? (Tutorial Page 1 Example #1) a) 3x + 1x b) 7x + 14x 5) Rewrite each equation in vertex form. (Tutorial Page 1 Example #) a) y = x + 8x + 13 c) y = x + 4x 3 MATHACHS TRIGONOMETRY SUMMER ASSIGNMENT JUNE, 017 Page 1

13 6) What are the solutions for each equation? Use the Quadratic Formula. (Tutorial Page Example #1 & ) a) x + 7x 3 = 0 b) x + 1 = 5 7x 7) Solve each system. (Tutorial Page 3 Example #1 & ) y< x + 6 a) y > x b) y= x x y = 3x ) What is the classification of each polynomial by its degree? By its number of terms? What is its end behavior? (Tutorial Page 4 Example #1) a) 8 6x 3 + 3x + x 3 b) 15x 7 7 MATHACHS TRIGONOMETRY SUMMER ASSIGNMENT JUNE, 017 Page 13

14 9) Find the real-number roots of each radical expression. (Tutorial Page 5 Example #1) a) b) ) Simplify each radical expression. Use absolute value symbols when needed. (Tutorial Page 5 Example #) a) 3 x 3 y b) 3 x 3 31) Simplify each product. (Tutorial Page 6 Example #1) a) 3 36x y 5 3 6x y b) 3 9x 5 y 3 x y 5 3) Rationalize the denominator of each expression. Assume that all variables are positive. (Tutorial Page 6 Example #) 19 a) 3 a b 4 9y b) abc 4 4 x MATHACHS TRIGONOMETRY SUMMER ASSIGNMENT JUNE, 017 Page 14

15 33) Simplify. (Tutorial Page 7 Example #1) a) b) 8 3 3x 3 4x x 34) Simplify. Rationalize all denominators. (Tutorial Page 7 Example #) a) (4 6 1)( 6 + 4) b) ) Simplify each expression. Assume that all variables are positive. (Tutorial Page 8 Example #1 & ) a) ( y )(3 y ) b) ( 3 x )(7 x ) MATHACHS TRIGONOMETRY SUMMER ASSIGNMENT JUNE, 017 Page 15

16 36) Write each expression in simplest form. Assume that all variables are positive. (Tutorial Page 8 Example #3) 16z 4 a) 5x 8 1 x b) y ) Solve. Check your solutions. (Tutorial Page 9 Example #1) a) 3 x = 3 b) 3 5x + 3 = 0 38) Solve. Check for extraneous solutions. (Tutorial Page 9 Example #) a) x 10 = x 5 b) x = x MATHACHS TRIGONOMETRY SUMMER ASSIGNMENT JUNE, 017 Page 16

17 39) Let f (x) = 4x 3 and g(x) = x +. Perform each function operation and then find the domain of the result. (Tutorial Page 30 Example #1 & ) a) (f g)(x) b) ( f g)(x) c) f(g()) d) f(g( 5)) 40) Find the inverse of each function. (Tutorial Page 31 Example #1) a) f( x) = x+ b) f(x) = x ) Name the domain and range of the inverse of the function. (Tutorial Page 31 Example #) a) y= x+ 5 b) y= 3 x + MATHACHS TRIGONOMETRY SUMMER ASSIGNMENT JUNE, 017 Page 17

18 4) Simplify each rational expression. State any restrictions on the variable. (Tutorial Page 3 Example #1) x + x 3x 1 a) b) x + x x x 6 43) Divide. State any restrictions on the variables. (Tutorial Page 33 Example #) 3x+ 1 x + 8x+ 16 a) x 8 x 8x+ 16 b) 4x 16 x x 8 4x 3x+ 6 44) Assume that the polynomials given are the denominators of rational expressions. Find the LCD of each set. (Tutorial Page 34 Example #1) a) x + 7x + 1 and x + 4 b) x 9 and x + x 3 MATHACHS TRIGONOMETRY SUMMER ASSIGNMENT JUNE, 017 Page 18

19 45) Simplify each sum or difference. State any restrictions on the variable. (Tutorial Page 34 Example #) x 3 a) b) + x + 5x + 6 x + 3x + x + x 4 46) Solve each equation. Check the solutions. (Tutorial Page 35 Example #1) a) + 6 = 6 x x 1 x x b) 4 5 x 1 = x 1 + MATHACHS TRIGONOMETRY SUMMER ASSIGNMENT JUNE, 017 Page 19

20 47) Find the center and radius of each circle. (Tutorial Page 36 Example #1) a) x + y + x 6y = 15 b) x + y 10x 4y = 0 48) Write each measure in radians and check. (Tutorial Page 37 Example #1) a) 150 b) 45 49) Write each measure in degrees and check. (Tutorial Page 37 Example #1) 7 a) π 6 b) 5 π 3 50) The measure θ of an angle in standard position is given. Find the exact values of cos θ and sin θ for each angle measure. (Tutorial Page 37 Example #) a) 3 π radians 4 b) π radians 3 MATHACHS TRIGONOMETRY SUMMER ASSIGNMENT JUNE, 017 Page 0

21 51) Use the unit circle to complete the following table. (Tutorial Page 38 & 39) a) θ in Degrees (Radians) Cosθ Sinθ Quadrant MATHACHS TRIGONOMETRY SUMMER ASSIGNMENT JUNE, 017 Page 1

22 5) Find the amplitude and period of each sine function. (Tutorial Page 40 Example #1) 1 a) y = sin 3 θ b) y = 4 4sin πθ 3 53) Graph each function. (Tutorial Page 40 Example #) 1 a) y = sin θ b) 1 y = sin θ 4 MATHACHS TRIGONOMETRY SUMMER ASSIGNMENT JUNE, 017 Page

23 54) Sketch the graph of each function in the interval from 0 to π. (Tutorial Page 41 Example #1) 1 1 a) y = cos πθ b) y = cos θ 4 55) Find the period and two asymptotes of the graph of each tangent function. Then find two points on each graph that are not on the x-axis. (Tutorial Page 4 Example #1) a) y = 4 tan θ b) y = tan θ 56) Graph at least three cycles of each tangent function. (Tutorial Page 43 Example #) a) y = 3 tan θ b) y = tan 4θ MATHACHS TRIGONOMETRY SUMMER ASSIGNMENT JUNE, 017 Page 3

24 57) Determine the amplitude, period, and any phase shift or vertical shift in the graphs of the functions. (Tutorial Page 44 Example #1) a) y = sin( x+ 3 π ) π π b) y = 3cos x ) Sketch each graph in the interval from 0 to π. (Tutorial Page 44 Example #) 1 a) y = sin x 1 b) y = cos3 x + π +1 59) Find the exact value of each expression. Do not use a calculator. (Tutorial Page 45 Example #1) a) sec 3π 4 b) csc π MATHACHS TRIGONOMETRY SUMMER ASSIGNMENT JUNE, 017 Page 4

25 60) Sketch each graph in the interval from 0 to π. (Tutorial Page 45 Example #) a) y = sec θ b) y = cot 3θ MATHACHS TRIGONOMETRY SUMMER ASSIGNMENT JUNE, 017 Page 5

Pre-Calculus Summer Assignment

Name: Pre-Calculus 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 Pre-Calculus.