Hmwk 13 over sec. 3.2

1/1/24, 5:28 PM Hmwk 13 over sec. 3.2-Rachel Chrisman https://tdx.acs.pearsonprd.tech/api/v1/print/highered 1/16 1. 2. 3. 4. Student: Rachel Chrisman Date: 01/01/24 Instructor: Robin Ayers Course: MATH 117 Trigonometry On Demand July 2023 - July 2025 Assignment: Hmwk 13 over sec. 3.2 Which of the following is the correct sum formula for the cosine function? Choose the correct answer. A. cos ( ) = sin cos + cos sin + B. cos ( ) = cos cos + sin sin + C. cos ( ) = sin cos − cos sin + D. cos ( ) = cos cos − sin sin + Which of the following is the correct difference formula for the sine function? Choose the correct answer. A. sin ( ) = cos cos − sin sin − B. sin ( ) = cos cos + sin sin − C. sin ( ) = sin cos − cos sin − D. sin ( ) = sin cos + cos sin − Which of the following is the correct sum formula for the tangent function? Choose the correct answer. A. tan ( ) = + tan − tan 1 + tan tan B. tan ( ) = + tan + tan 1 − tan tan C. tan ( ) = + tan + tan 1 + tan tan D. tan ( ) = + tan − tan 1 − tan tan Which of the following is the correct difference formula for the tangent function? Choose the correct answer. A. tan ( ) = − tan − tan 1 − tan tan B. tan ( ) = − tan − tan 1 + tan tan C. tan ( ) = − tan + tan 1 + tan tan D. tan ( ) = − tan + tan 1 − tan tan

1/1/24, 5:28 PM Hmwk 13 over sec. 3.2-Rachel Chrisman https://tdx.acs.pearsonprd.tech/api/v1/print/highered 2/16 5. 6. 7. 8. 9. 10. Which of the following can best be evaluated using the sum formula for the sine function? Choose the correct answer. A. sin tan − 1 1 + cos − 1 3 2 B. sin 1 2 cos − 1 − 1 2 C. cos 2 sin − 1 − 1 2 D. sin cos − 1 − 1 2 Simplify the expression. + − 3 2 1 2 1 2 − 1 2 + − 3 2 1 2 1 2 − 1 2 = (Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression.) Simplify the expression. − 1 − − 7 1 + ( − 1) − 7 − 1 − − 7 1 + ( − 1) − 7 = (Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression.) Simplify the expression. + − 5 61 − 3 58 − 6 61 7 58 + − 5 61 − 3 58 − 6 61 7 58 = (Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression.) Find the exact value of the trigonometric expression without the use of a calculator. cos + 6 4 cos + 6 4 = (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Do not factor.) Find the exact value of the trigonometric expression without the use of a calculator. cos (60 ° + 45 ° ) cos (60 ° + 45 ° ) = (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Do not factor.)

1/1/24, 5:28 PM Hmwk 13 over sec. 3.2-Rachel Chrisman https://tdx.acs.pearsonprd.tech/api/v1/print/highered 4/16 15. Use the cosine of the difference of two angles formula to find the exact value of the trigonometric expression without the use of a calculator. cos 13 12 Write the angle as the difference of two angles. 13 12 5 6 6 5 4 2 2 3 3 3 2 4 Drag all correct angles into the boxes provided. cos 13 12 = cos ( − ) Enter the appropriate angles into the correct formula for the cosine of the difference of two angles. Select the correct choice below and fill in the answer boxes to complete your choice. (In each term, type the smaller angle in the first box and the larger angle in the second box.) A. cos = cos cos − sin sin 13 12 B. cos = sin cos + sin cos 13 12 C. cos = cos cos + sin sin 13 12 D. cos = sin cos − sin cos 13 12 Choose and complete the correct formula below by typing the correct value in each of the four parentheses. Each of the four parentheses represents the exact value of a trigonometric expression seen in the correct formula from the previous step. Select the correct choice below and fill in the answer boxes to complete your choice. (Type exact answers, using radicals as needed. Use integers or fractions for any numbers in the expression.) A. cos = + 13 12 B. cos = − 13 12

1/1/24, 5:28 PM Hmwk 13 over sec. 3.2-Rachel Chrisman https://tdx.acs.pearsonprd.tech/api/v1/print/highered 5/16 16. 17. 18. Use the cosine of the sum of two angles formula to find the exact value of the trigonometric expression without the use of a calculator. cos (105 ° ) 60 ° 90 ° 270 ° 135 ° 30 ° 120 ° 150 ° 45 ° Drag appropriate angles to create the cosine of the sum of two angles given above into the appropriate area below. Place the smaller angle into the first box and place the larger angle into the second box. cos (105 ° ) = cos ( + ) Enter the appropriate angles into the correct formula for the cosine of the sum of two angles. Select the correct choice below and fill in the answer boxes to complete your choice. (In each term, type the smaller angle in the first box and the larger angle in the second box.) A. cos (105 ° ) = cos ° cos ° − sin ° sin ° B. cos (105 ° ) = cos ° sin ° + cos ° sin ° C. cos (105 ° ) = cos ° cos ° + sin ° sin ° D. cos (105 ° ) = cos ° sin ° − cos ° sin ° Choose and complete the correct formula below by typing the correct value in each of the four parentheses. Each of the four parentheses represents the exact value of a trigonometric expression seen in the correct formula from the previous step. Select the correct choice below and fill in the answer boxes to complete your choice. (Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression.) A. cos (105 ° ) = − • • B. cos (105 ° ) = + • • cos (105 ° ) = (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Do not factor.) Suppose that the terminal side of angle lies in Quadrant I and the terminal side of angle lies in Quadrant IV. If and , find the exact value of . sin = 5 13 cos = 6 85 cos ( + ) cos ( + ) = (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.) Suppose that the terminal side of angle lies in Quadrant II and the terminal side of angle lies in Quadrant I. If and , find the exact value of . tan = − 7 24 cos = 5 6 cos ( − ) cos ( − ) = (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Do not factor.)

1/1/24, 5:28 PM Hmwk 13 over sec. 3.2-Rachel Chrisman https://tdx.acs.pearsonprd.tech/api/v1/print/highered 7/16 25. Use the sine of the difference of two angles formula to find the exact value of the following trigonometric expression without the use of a calculator. sin 13 12 2 3 2 2 3 4 6 5 6 5 4 3 A list of angles belonging to the four special angle families is given. Drag one angle into each of the boxes provided to create an equivalent expression involving the sine of the difference of two angles. sin 13 12 = sin − Enter the appropriate angles into the correct formula for the sine of the difference of two angles. Select the correct choice below and fill in the answer boxes to complete your choice. A. sin 13 12 = sin cos + cos sin B. sin 13 12 = cos cos + sin sin C. sin 13 12 = sin cos − cos sin D. sin 13 12 = cos cos − sin sin Choose and complete the correct formula below by typing the correct value in each of the four parentheses. Each of the four parentheses represents the exact value of a trigonometric expression seen in the correct formula from the previous step. Select the correct choice below and fill in the answer boxes to complete your choice. (Type the exact values for the trigonometric expressions in the same order that the expressions appear in the previous step. Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression.) A. sin 13 12 = + B. sin 13 12 = −

1/1/24, 5:28 PM Hmwk 13 over sec. 3.2-Rachel Chrisman https://tdx.acs.pearsonprd.tech/api/v1/print/highered 8/16 26. 27. 28. Use the sine of the sum of two angles formula to find the exact value of each trigonometric expression without the use of a calculator. sin (165 ° ) 135 ° 45 ° 30 ° 150 ° 270 ° 300 ° 90 ° 60 ° Drag the smaller angle into the first box and the larger angle into the second box from the list of angles given above into the appropriate area below to create the sine of the sum of two angles. sin (165 ° ) = sin + Enter the appropriate angles into the correct formula for the sine of the sum of two angles. Select the correct choice below and fill in the answer boxes to complete your choice. (In each term, type the smaller angle in the first box and the larger angle in the second box. ) A. sin (165 ° ) = sin ° cos ° − cos ° sin ° B. sin (165 ° ) = sin ° cos ° + cos ° sin ° C. sin (165 ° ) = cos ° cos ° − sin ° sin ° D. sin (165 ° ) = cos ° cos ° + sin ° sin ° Choose and complete the correct formula below by typing the correct value in each of the four parentheses. Each of the four parentheses represents the exact value of a trigonometric expression seen in the correct formula from the previous step. Select the correct choice below and fill in the answer boxes to complete your choice. (Type the exact values for the trigonometric expressions in the same order that the expressions appear in the previous step. Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression.) A. sin (165 ° ) = + B. sin (165 ° ) = − Simplify. sin (165 ° ) = (Simplify your answer. Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression.) Suppose that the terminal side of angle lies in Quadrant I and the terminal side of angle lies in Quadrant IV. If and , find the exact value of . sin = 3 5 cos = 8 113 sin ( + ) sin ( + ) = (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.) Suppose that is an angle such that and . Also, suppose that is an angle such that and 0. Find the exact value of . tan = 3 5 sin < 0 cot = − 2 9 sec < sin ( − ) sin ( − ) = (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)

1/1/24, 5:28 PM Hmwk 13 over sec. 3.2-Rachel Chrisman https://tdx.acs.pearsonprd.tech/api/v1/print/highered 10/16 35. Use the sine of the difference of two angles formula to find the exact value of the following trigonometric expression without the use of a calculator. sin 5 12 5 2 6 3 2 3 5 4 4 3 2 2 A list of angles belonging to the four special angle families is given. Drag one angle into each of the boxes provided to create an equivalent expression involving the sine of the difference of two angles. sin 5 12 = sin − Enter the appropriate angles into the correct formula for the sine of the difference of two angles. Select the correct choice below and fill in the answer boxes to complete your choice. A. sin 5 12 = cos cos + sin sin B. sin 5 12 = sin cos + cos sin C. sin 5 12 = cos cos − sin sin D. sin 5 12 = sin cos − cos sin Choose and complete the correct formula below by typing the correct value in each of the four parentheses. Each of the four parentheses represents the exact value of a trigonometric expression seen in the correct formula from the previous step. Select the correct choice below and fill in the answer boxes to complete your choice. (Type the exact values for the trigonometric expressions in the same order that the expressions appear in the previous step. Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression.) A. sin 5 12 = − B. sin 5 12 = +

1/1/24, 5:28 PM Hmwk 13 over sec. 3.2-Rachel Chrisman https://tdx.acs.pearsonprd.tech/api/v1/print/highered 11/16 36. 37. 38. Use the sine of the sum of two angles formula to find the exact value of each trigonometric expression without the use of a calculator. sin (255 ° ) 270 ° 90 ° 60 ° 150 ° 30 ° 300 ° 225 ° 45 ° Drag the smaller angle into the first box and the larger angle into the second box from the list of angles given above into the appropriate area below to create the sine of the sum of two angles. sin (255 ° ) = sin + Enter the appropriate angles into the correct formula for the sine of the sum of two angles. Select the correct choice below and fill in the answer boxes to complete your choice. (In each term, type the smaller angle in the first box and the larger angle in the second box. ) A. sin (255 ° ) = cos ° cos ° + sin ° sin ° B. sin (255 ° ) = sin ° cos ° − cos ° sin ° C. sin (255 ° ) = sin ° cos ° + cos ° sin ° D. sin (255 ° ) = cos ° cos ° − sin ° sin ° Choose and complete the correct formula below by typing the correct value in each of the four parentheses. Each of the four parentheses represents the exact value of a trigonometric expression seen in the correct formula from the previous step. Select the correct choice below and fill in the answer boxes to complete your choice. (Type the exact values for the trigonometric expressions in the same order that the expressions appear in the previous step. Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression.) A. sin (255 ° ) = + B. sin (255 ° ) = − Simplify. sin (255 ° ) = (Simplify your answer. Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression.) Suppose that the terminal side of angle lies in Quadrant I and the terminal side of angle lies in Quadrant IV. If and , find the exact value of . sin = 7 25 cos = 8 89 sin ( + ) sin ( + ) = (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.) Suppose that is an angle such that and . Also, suppose that is an angle such that and 0. Find the exact value of . tan = 3 8 cos < 0 cot = − 2 5 csc > sin ( − ) sin ( − ) = (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)

1/1/24, 5:28 PM Hmwk 13 over sec. 3.2-Rachel Chrisman https://tdx.acs.pearsonprd.tech/api/v1/print/highered 13/16 46. 47. Use the tangent of the difference of two angles formula to find the exact value of the trigonometric expression without the use of a calculator. tan ( ) 165 ° 45 ° 225 ° 30 ° 315 ° 180 ° 60 ° 90 ° 270 ° Drag appropriate angles to create the tangent of the difference of two angles given above into the appropriate area below, the larger angle goes into the first box and the smaller angle into the second box. tan ( ) 165 ° = tan ( − ) Enter the appropriate angles into the correct formula for the tangent of the difference of two angles. Select the correct choice below and fill in the answer boxes to complete your choice. (In each term, type the larger angle in the first box and the smaller angle in the second box.) A. tan ( ) 165 ° = tan ° + tan ° 1 − tan ° tan ° B. tan ( ) 165 ° = 1 + tan ° tan ° tan ° − tan ° C. tan ( ) 165 ° = 1 − tan ° tan ° tan ° + tan ° D. tan (165 ° ) = tan ° − tan ° 1 + tan ° tan ° (Type an integer or a fraction.) Choose the complete correct formula below by typing the correct value in each of the four parentheses. Each of the four parentheses represents the exact value of a trigonometric expression seen in the correct formula from the previous step. Select the correct choice below and fill in the answer boxes to complete your choice. (Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression.) A. tan ( ) = 165 ° 1 − + B. tan (165 ° ) = − 1 + C. tan ( ) = 165 ° 1 + − D. tan ( ) = 165 ° + 1 − (Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression.) Suppose that the terminal side of angle lies in Quadrant and the terminal side of angle lies in Quadrant . If and , find the exact value of . IV III sin = − 1 6 cos = − 5 13 tan ( + ) tan ( + ) = (Simplify your answer. Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression.)

1/1/24, 5:28 PM Hmwk 13 over sec. 3.2-Rachel Chrisman https://tdx.acs.pearsonprd.tech/api/v1/print/highered 14/16 48. 49. Verify the identity. sin + = cos 2 Which of the following is a correct sequence of steps that verifies the given identity? A. sin + = sin cos − cos sin = ( ) cos − ( ) sin = cos 2 2 2 1 0 B. sin + = sin cos + cos sin = ( ) cos + ( ) sin = cos 2 2 2 1 0 C. sin + = sin cos − cos sin = ( ) cos − ( ) sin = cos 2 3 2 3 2 − 1 0 D. sin + = sin cos + cos sin = ( ) cos + ( ) sin = cos 2 3 2 3 2 1 0 Verify the identity. = cot + tan cos ( − ) cos sin Which of the following is a correct sequence of steps that verifies the given identity? A. cos ( − ) cos sin = sin cos + cos sin cos sin = sin cos cos sin + cos sin cos sin = cot + tan B. cos ( − ) cos sin = cos cos − sin sin cos sin = cos cos cos sin − sin sin cos sin = cot + tan C. cos ( − ) cos sin = cos cos + sin sin sin cos = cos cos sin cos + sin sin sin cos = cot + tan D. cos ( − ) cos sin = cos cos + sin sin cos sin = cos cos cos sin + sin sin cos sin = cot + tan

1/1/24, 5:28 PM Hmwk 13 over sec. 3.2-Rachel Chrisman https://tdx.acs.pearsonprd.tech/api/v1/print/highered 16/16 51. 52. 53. Verify the identity. cot ( − ) = cot cot + 1 cot − cot Which of the following is a correct sequence of steps that verifies the given identity? A. cot ( − ) = = = cos ( − ) sin ( − ) cos cos + sin sin sin cos − cos sin cos cos + sin sin sin sin sin cos − cos sin sin sin = = cos cos sin sin + sin sin sin sin sin cos sin sin − cos sin sin sin cot cot + 1 cot − cot B. cot ( − ) = = = sin ( − ) cos ( − ) sin cos + cos sin cos cos − sin sin sin cos + cos sin sin sin cos cos − sin sin sin sin = = sin cos sin sin + cos sin sin sin cos cos sin sin − sin sin sin sin cot cot + 1 cot − cot C. cot ( − ) = = = cos ( − ) sin ( − ) cos cos + sin sin sin cos − cos sin cos cos + sin sin cos cos sin cos − cos sin cos cos = = cos cos cos cos + sin sin cos cos sin cos cos cos − cos sin cos cos cot cot + 1 cot − cot Find the exact value of the expression without the use of a calculator. cos sin − 1 3 5 + cos − 1 − 4 5 (Type an exact answer in simplified form.) cos sin − 1 3 5 + cos − 1 − 4 5 = Find the exact value of the trigonometric expression without the use of a calculator. tan sin − + cos − − 1 1 2 − 1 3 2 tan sin − + cos − − 1 1 2 − 1 3 2 = (Simplify your answer. Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression.)