Hmwk 7 over sec. 2.1

1/1/24, 5:07 PM Hmwk 7 over sec. 2.1-Rachel Chrisman https://tdx.acs.pearsonprd.tech/api/v1/print/highered 1/14 1. 2. 3. 4. 5. Student: Rachel Chrisman Date: 01/01/24 Instructor: Robin Ayers Course: MATH 117 Trigonometry On Demand July 2023 - July 2025 Assignment: Hmwk 7 over sec. 2.1 Which of the following is not a characteristic of the sine function? Choose the correct answer. A. The sine function is an odd function, which means that . sin ( ) = − sin x − x B. The y-intercept of the sine function is 0. C. The x-intercepts or zeros of the sine function are of the form where n is an integer. x = n D. The sine function obtains a relative maximum at where n is an integer. x = + n 2 Which of the following is not a characteristic of the cosine function? Choose the correct answer. A. The cosine function obtains a relative maximum at where n is an integer. x = 2 n B. The cosine function is an even function, which means that . cos ( ) = cos x − x C. The x-intercepts or zeros of the cosine function are of the form where n is an integer. x = ( ) 2n + 1 2 D. The y-intercept is 0. Which of the following statements describes the definition of amplitude of a sine or cosine function? Choose the correct answer. A. The amplitude is the measure of half the distance between the maximum and minimum values. B. The amplitude measures the distance between the maximum and minimum values. C. The amplitude is the minimum value of the sine or cosine function. D. The amplitude is the maximum value of the sine or cosine function. If where , then which of the following statements is true? y = sin ( ) Bx B > 0 Choose the correct answer. A. The period of is the length of the interval that results from the solution to the three-part inequality . y = sin ( ) Bx − 2 ≤ Bx ≤ 2 B. The period of is the length of the interval that results from the solution to the three-part inequality . y = sin ( ) Bx 0 ≤ Bx ≤ 2 C. The period of is always equal to regardless of the value of B . y = sin ( ) Bx 2 D. The period of is the length of the interval that results from the solution to the three-part inequality . y = sin ( ) Bx 0 ≤ Bx ≤ Which of the following statements is not true about the function ? y = A cos ( ) Bx Choose the correct answer. A. The amplitude is . A B. The period is . P = 2 B C. The range is . [ ] − A , A D. If , then the function is equivalent to the function . B > 0 y = A cos ( ) − Bx y = − A cos ( ) Bx

1/1/24, 5:07 PM Hmwk 7 over sec. 2.1-Rachel Chrisman https://tdx.acs.pearsonprd.tech/api/v1/print/highered 2/14 6. 7. Sketch the graph of and identify the properties that apply. y = sin x Choose the correct graph of the function. A. -2 2 y x B. -2 2 x y C. -2 2 y i. Is the function an function? even Yes No ii. Is the function on the interval ? decreasing , 2 No Yes iii. Is the of the function ? range ( − 1,1) Yes No iv. Is the y-intercept ? 0 Yes No v. Are the zeros of the form , where n is any integer? 2n + 1 2 Yes No vi. Does the function obtain a relative at , where n is any integer? maximum x = 2 n No Yes YOU ANSWERED: Yes Yes Using the graph of , list all values on the interval that satisfy the ordered pair . y = sin x − 5 4 , 11 3 (x,0) List all the values that satisfy . (x,0) − 3 , − 2 , − ,0, (Type an exact answer using as needed. Use a comma to separate answers as needed. Use integers or fractions for any numbers in the expression.) − 2 2 − 2 2 − 2

1/1/24, 5:07 PM Hmwk 7 over sec. 2.1-Rachel Chrisman https://tdx.acs.pearsonprd.tech/api/v1/print/highered 4/14 12. 13. 14. Use the periodic property of to determine which of the following expressions is equivalent to . y = cos x cos − 8 5 i. cos 2 5 ii. cos − 5 iii. cos 13 5 iv. cos 6 5 Choose the correct answer below. cos 6 5 cos 13 5 cos 2 5 cos − 5 Use the periodic property of to determine which of the following expressions is equivalent to . y = cos x cos − 22 7 i. cos 5 7 ii. cos − 8 7 iii. cos 3 7 iv. cos − 17 7 Choose the correct answer below. cos − 17 7 cos 5 7 cos 3 7 cos − 8 7 Determine the amplitude and range of the function and sketch its graph. y = 7 sin x The amplitude is . 7 The range is . [ − 7,7] (Type your answer in interval notation.) The coordinates of the five quarter points for are given below. Use these quarter points to determine the y-coordinates of the quarter points of . y = sin x y = 7 sin x y = sin x (0,0) ,1 2 ( ,0) , − 1 3 2 (2 ,0) y = 7 sin x 0, 0 , 2 7 , 0 , 3 2 − 7 2 , 0 Choose the correct graph of below. y = 7 sin x A. -8 8 x y B. -8 8 x y C. -8 8 y 2 2

1/1/24, 5:07 PM Hmwk 7 over sec. 2.1-Rachel Chrisman https://tdx.acs.pearsonprd.tech/api/v1/print/highered 5/14 15. 16. Determine the amplitude and range of the function and sketch its graph. y = 5 cos x The amplitude is . 5 The range is . [ − 5,5] (Type your answer in interval notation.) The coordinates of the five quarter points for are given below. Use these quarter points to determine the y-coordinates of the quarter points of . y = cos x y = 5 cos x y = cos x (0,1) ,0 2 ( , − 1) ,0 3 2 (2 ,1) y = 5 cos x 0, 5 , 2 0 , − 5 , 3 2 0 2 , 5 Choose the correct graph of below. y = 5 cos x A. -6 6 x y B. -6 6 x y C. -6 6 y YOU ANSWERED: B. Determine the amplitude and range of the function and sketch its graph. y = cos x 1 4 The amplitude is . 1 4 The range is . − , 1 4 1 4 (Type your answer in interval notation.) The coordinates of the five quarter points for are given below. Use these quarter points to determine the y-coordinates of the quarter points of . y = cos x y = cos x 1 4 y = cos x (0,1) ,0 2 ( , − 1) ,0 3 2 (2 ,1) y = cos x 1 4 0, , 2 , , 3 2 2 , Choose the correct graph of below. y = cos x 1 4 A. -0.25 0.25 x y B. -0.25 0.25 x y C. -0.25 0.25 y 2 2 2 2

1/1/24, 5:07 PM Hmwk 7 over sec. 2.1-Rachel Chrisman https://tdx.acs.pearsonprd.tech/api/v1/print/highered 7/14 22. 23. 24. 25. Determine the period of the function and sketch its graph. y = cos (3x) The period is . 2 3 (Simplify your answer. Type an exact answer, using as needed. Use integers or fractions for any numbers in the expression.) The coordinates of the five quarter points for are given below. Use these quarter points to determine the x-coordinates of the quarter points of . y = cos x y = cos (3x) y = cos x (0,1) ,0 2 ( , − 1) ,0 3 2 (2 ,1) y = cos (3x) ,1 ,0 , − 1 ,0 ,1 (Simplify your answers. Type exact answers, using as needed. Use integers or fractions for any numbers in the expressions.) Choose the correct graph of below. y = cos (3x) A. -1.5 1.5 x y B. -1.5 1.5 x y C. -1.5 1.5 y Determine the period of the function and sketch its graph. y = cos ( − 3x) The period is . (Simplify your answer. Type an exact answer, using as needed. Use integers or fractions for any numbers in the expression.) The coordinates of the five quarter points for are given below. Use these quarter points to determine the x-coordinates of the quarter points of . y = cos x y = cos ( − 3x) y = cos x (0,1) ,0 2 ( , − 1) ,0 3 2 (2 ,1) y = cos ( − 3x) ,1 ,0 , − 1 ,0 ,1 (Simplify your answers. Type exact answers, using as needed. Use integers or fractions for any numbers in the expressions.) Choose the correct graph of below. y = cos ( − 3x) A. -1.5 1.5 x y B. -1.5 1.5 x y C. -1.5 1.5 y Determine the period of the function and sketch its graph. y = sin ( − 2 x) The period is . 1 (Simplify your answer. Type an exact answer, using as needed. Use integers or fractions for any numbers in the expression.) The coordinates of the five quarter points for are given below. Use these quarter points to determine the x-coordinates of the quarter points of . y = sin x y = sin ( − 2 x) y = sin x (0,0) ,1 2 ( ,0) , − 1 3 2 (2 ,0) y = sin ( − 2 x) ,0 , − 1 ,0 ,1 ,0 (Simplify your answers. Type exact answers, using as needed. Use integers or fractions for any numbers in the expressions.) Choose the correct graph of below. y = sin ( − 2 x) A. -1.5 1.5 x y B. -1.5 1.5 x y C. -1.5 1.5 y Determine the amplitude of the function . y = cos ( − x) The amplitude is . 1 2 3 6 2 3 2 3 1 1

1/1/24, 5:07 PM Hmwk 7 over sec. 2.1-Rachel Chrisman https://tdx.acs.pearsonprd.tech/api/v1/print/highered 8/14 26. 27. 28. 29. Determine the range of the function . y = cos − x 1 3 The range is . [ − 1,1] (Type your answer in interval notation. Use integers or fractions for any numbers in the expression. Simplify your answer.) Determine the coordinates for the five quarter points of the function that correspond to the five quarter points of . y = cos (2x) cos x The coordinates of the five quarter points for are given below. Use these quarter points to determine the y-coordinates of the quarter points of . y = cos x y = cos (2x) (0,1) ,0 2 ( , − 1) ,0 3 2 (2 ,1) (Type ordered pairs. Type exact answers, using as needed. Use integers or fractions for any numbers in the expressions.) Determine the amplitude, range, and period of the function and sketch its graph. y = 3 cos (2x) The amplitude is . (Type an integer or a fraction.) The range is . (Type your answer in interval notation. Use integers or fractions for any numbers in the expression. Simplify your answer.) The period is . (Type an exact answer, using as needed. Use integers or fractions for any numbers in the expression.) The coordinates of the five quarter points for are given below. Use these quarter points to determine the y-coordinates of the quarter points of . y = cos x y = 3 cos (2x) (0,1) ,0 2 ( , − 1) ,0 3 2 (2 ,1) (Type ordered pairs. Type exact answers, using as needed. Use integers or fractions for any numbers in the expressions.) Choose the correct graph of below. y = 3 cos (2x) A. -4 4 x y B. -4 4 x y C. -4 4 y Determine the amplitude, range, and period of the function and sketch its graph. y = − cos (3x) 4 3 The amplitude is . (Type an integer or a fraction.) The range is . (Type your answer in interval notation. Use integers or fractions for any numbers in the expression. Simplify your answer.) The period is . (Type an exact answer, using as needed. Use integers or fractions for any numbers in the expression.) The coordinates of the five quarter points for are given below. Use these quarter points to determine the y-coordinates of the quarter points of . y = cos x y = − cos (3x) 4 3 (0,1) ,0 2 ( , − 1) ,0 3 2 (2 ,1) (Type ordered pairs. Type exact answers, using as needed. Use integers or fractions for any numbers in the expressions.) Choose the correct graph of below. y = − cos (3x) 4 3 A. -1.5 1.5 x y B. -1.5 1.5 x y C. -1.5 1.5 y 4 2 3 2 3

1/1/24, 5:07 PM Hmwk 7 over sec. 2.1-Rachel Chrisman https://tdx.acs.pearsonprd.tech/api/v1/print/highered 10/14 32. 33. 34. 35. Determine the amplitude, range, and period of the function and sketch its graph. y = − 5 cos x 5 4 The amplitude is . The range is . (Simplify your answer. Type your answer in interval notation. Use integers or fractions for any numbers in the expression.) The period is . (Type an exact answer, using as needed. Use integers or fractions for any numbers in the expression.) The coordinates of the five quarter points for are given below. Use these quarter points to determine the y-coordinates of the quarter points of . y = cos x y = − 5 cos x 5 4 (0,1) ,0 2 ( , − 1) ,0 3 2 (2 ,1) (Type ordered pairs. Type exact answers, using as needed. Use integers or fractions for any numbers in the expressions.) Choose the correct graph of below. y = − 5 cos x 5 4 A. -6 6 x y B. -6 6 x y C. -6 6 y Determine the amplitude, range, and period of the function and sketch its graph. y = 5 cos x 4 The amplitude is . 5 The range is . [ − 5,5] (Type your answer in interval notation. Use integers or fractions for any numbers in the expression. Simplify your answer.) The period is . 8 (Type an exact answer, using as needed. Use integers or fractions for any numbers in the expression.) The coordinates of the five quarter points for are given below. Use these quarter points to determine the y-coordinates of the quarter points of . y = cos x y = 5 cos x 4 (0,1) ,0 2 ( , − 1) ,0 3 2 (2 ,1) (Type ordered pairs. Type exact answers, using as needed. Use integers or fractions for any numbers in the expressions.) Choose the correct graph of below. y = 5 cos x 4 A. -6 6 x y B. -6 6 x y C. -6 6 y Determine the amplitude of the function . y = − cos (2x) 2 3 The amplitude is . (Type an integer or a fraction.) 2 3 Determine the range of the function . y = − 7 sin x 7 4 The range of the function is . y = − 7 sin x 7 4 [ − 7,7] (Simplify your answer. Type your answer in interval notation.) 5 2 8 5 8 1 2

1/1/24, 5:07 PM Hmwk 7 over sec. 2.1-Rachel Chrisman https://tdx.acs.pearsonprd.tech/api/v1/print/highered 11/14 36. 37. 38. 39. 40. 41. Determine the period of the function . y = − 6 cos x 7 6 The period of the function is . y = − 6 cos x 7 6 12 7 (Simplify your answer. Type an exact answer, using as needed. Use integers or fractions for any numbers in the expression.) Determine the coordinates for the five quarter points of the function that correspond to the five quarter points of . y = − 4 cos (3 x) y = cos x The coordinates of the five quarter points for are given below. Use these quarter points to determine the y-coordinates of the quarter points of . y = cos x y = − 4 cos (3 x) (0,1) ,0 2 ( , − 1) ,0 3 2 (2 ,1) (Type ordered pairs. Type exact answers, using as needed. Use integers or fractions for any numbers in the expressions.) Sketch the graph of the function . y = 2 sin (5x) Choose the correct graph below. A. -3 3 x y B. -3 3 x y C. -3 3 y Sketch the graph of the function . y = sin x 3 2 1 4 Choose the correct graph below. A. -2 2 x y B. -2 2 x y C. -2 2 y Sketch the graph of the function . y = − sin − x 3 2 Choose the correct graph below. A. -1.5 1.5 x y B. -1.5 1.5 x y C. -1.5 1.5 y Sketch the graph of the function . y = 2 cos − x 4 Choose the correct graph below. A. -3 3 x y B. -3 3 x y C. -3 3 y 10 2 5 8 8 4 3 4 3 8 1 2

1/1/24, 5:07 PM Hmwk 7 over sec. 2.1-Rachel Chrisman https://tdx.acs.pearsonprd.tech/api/v1/print/highered 13/14 45. 46. 47. 48. One cycle of the graph of a trigonometric function of the form y or y is given. Determine the equation of the function represented by the following graph. = A sin (Bx) = A cos (Bx) -8 -6 -4 -2 2 4 6 8 x y What function of the form y or y , B 0 is represented by the given graph? = A sin (Bx) = A cos (Bx) > (Use integers or fractions for any numbers in the equation.) One cycle of the graph of a trigonometric function of the form y or y is given. Determine the equation of the function represented by the following graph. = A sin (Bx) = A cos (Bx) -1 -0.8 -0.6 -0.4 -0.2 0.2 0.4 0.6 0.8 1 x y What function of the form y or y , B 0 is represented by the given graph? = A sin (Bx) = A cos (Bx) > (Use integers or fractions for any numbers in the equation.) One cycle of the graph of a trigonometric function of the form y or y is given. Determine the equation of the function represented by the following graph. = A sin (Bx) = A cos (Bx) -2 2 x y What function of the form y or y , B 0 is represented by the given graph? = A sin (Bx) = A cos (Bx) > (Use integers or fractions for any numbers in the equation.) One cycle of the graph of a trigonometric function of the form y or y is given. Determine the equation of the function represented by the following graph. = A sin (Bx) = A cos (Bx) -2 2 x y What function of the form y or y , B 0 is represented by the given graph? = A sin (Bx) = A cos (Bx) > (Use integers or fractions for any numbers in the equation.) − 2 2 (0, − 2) ( ,2) − 2 2 0, 1 2 , − 1 2 − 8 4 2 (0,1) 4 , − 1 − ( ,1) (3 , − 1) 2 4

1/1/24, 5:07 PM Hmwk 7 over sec. 2.1-Rachel Chrisman https://tdx.acs.pearsonprd.tech/api/v1/print/highered 14/14 49. 50. 51. 52. One cycle of the graph of a trigonometric function of the form y or y is given. Determine the equation of the function represented by the following graph. = A sin (Bx) = A cos (Bx) -8 -6 -4 -2 2 4 6 8 x y What function of the form y or y , B 0 is represented by the given graph? = A sin (Bx) = A cos (Bx) > (Use integers or fractions for any numbers in the equation.) One cycle of the graph of a trigonometric function of the form y or y is given. Determine the equation of the function represented by the following graph. = A sin (Bx) = A cos (Bx) -8 -6 -4 -2 2 4 6 8 x y What function of the form y or y , B 0 is represented by the given graph? = A sin (Bx) = A cos (Bx) > (Use integers or fractions for any numbers in the equation.) One cycle of the graph of a trigonometric function of the form y or y is given. Determine the equation of the function represented by the following graph. = A sin (Bx) = A cos (Bx) -8 -6 -4 -2 2 4 6 8 x y What function of the form y or y , B 0 is represented by the given graph? = A sin (Bx) = A cos (Bx) > (Use integers or fractions for any numbers in the equation.) One cycle of the graph of a trigonometric function of the form y or y is given. Determine the equation of the function represented by the following graph. = A sin (Bx) = A cos (Bx) -8 -6 -4 -2 2 4 6 8 x y What function of the form y or y , B 0 is represented by the given graph? = A sin (Bx) = A cos (Bx) > (Use integers or fractions for any numbers in the equation.) − 4 2 4 ,5 3 4 , − 5 − 10 5 2 5 (0, − 3) 5 ,3 − 5 2 5 2 ,5 15 2 , − 5 5 10 − 3 2 3 2 , − 2 9 2 ,2 3 6