Title Trigonometry-Trigonometric Algebra Unit 2 -Assessment-Solutions.pdf ✅

TRIGONOMETRY – UNIT 2 TRIGONOMETRIC ALGEBRA UNIT UNIT ASSESSMENT -SOLUTIONS (Use calculator if necessary) 1. On which of the following intervals would y x = sin ( ) not be one-to-one? (1) 0 90     x (3) −     90 90 x (2) −     90 0 x (4) 0 180     x 2. Which of the following values is not in the domain of the inverse cosine function? (1) 1 (3) 3 2 (2) 4 5 (4) 1 2 − 3. To the nearest degree, which of the following is the solution set to 3cos 1 0 ( A) − = on the interval 0 360    A ? (1) 71 , 289   (3) 109 , 251   (2) 71 ,109   (4) 109 , 289   4. Which of the following equations will have no real solutions? (1) 5cos 3 0 ( x) − = (3) 3sin 8 0 ( x) − = (2) 6sin 1 0 ( x) + = (4) 4cos 4 0 ( x) + = 5. The value of ( ) 2 tan 30 is which of the following? (1) 2 3 (3) 3 2 (2) 1 3 (4) 4 3 (4) The domain of the inverse cosine is the same as the range of cosine, which is all values from -1 to 1, inclusive. The only value that doesn’t fall in this range is choice (3). (3) (1) (3) (2)
6. If 5 cos 3 B = and sin 0 (B)  , then which of the following is the value of sin (B) ? (1) 2 9 (3) 2 3 (2) 2 3 (4) 4 9 7. Which of the following is equivalent to sin 55 cos 15 sin 15 cos 55 (   +   ) ( ) ( ) ( ) ? (1) sin 70 ( ) (3) cos 70 ( ) (2) sin 30 ( ) (4) cos 30 ( ) 8. If sin 0.8 ( A) = − then which of the following is the value of cos 2( A) ? (1) 1.22 (3) −0.28 (2) 0.34 (4) −1.6 9. Which of the following is a solution to the equation (sin 3 sin 1 0 x x − + = )( ) ? (1) 45 (3) 270 (2) 60 (4) 360 10. The graph of the function 3 7cos 3 2 x y   = − +     is shown below. Which of the following is closest to the smallest solution to the equation 3 7cos 3 0 2   x − + =     on the interval 0 360     x ? (1) 43 (2) 62 (3) 87 (4) 120 (2) (1) (3) (3) The smallest solution will correspond to the zero farthest to the left on the graph. This is clearly between and on the graph. So, the best choice would be (1). (1)
11. Algebraically solve the following equation for all values of  on the interval 0 360      . 2 cos 1 0 ( ) − = (1) {30°, 330°} (2) {45°, 315°} (3) {60°, 300°} (4) {90°, 270°} 12. Algebraically solve the following equation for all value(s) of x on the interval 0 360     x . Round all non- integer answers to the nearest tenth of a degree. 2 6sin sin 1 0 x x − − = (1) {45°, 135°, 224.5°} (2) {25.2°, 154.8°, 205.2°, 234/8°} (3) {60.8°, 119.2°} (4) {30°, 150°, 199.5°, 340.5°} 13. How many solutions will the equation below have on the interval 0 360     x ? 2 sin 4cos 4 0 x x + + = (1) None (2) one (3) Two (4) Three There will be only one solution. This problem could also be solved graphically. (2) (4) (2)
Questions 14 to 16 are based on the information given below. If 7 cos 4 A = − and 90 180     A then find the values of each of the following. Round all non-integer answers to the nearest hundredth of a degree. 14. sin A (1) 0.25 (2) 0.5 (3) 0.75 (4) 0.95 15. sin 2( A) (1) -0.99 (2) -0.83 (3) 0.71 (4) 0.97 16. cos 2( A) (1) -0.13 (2) -0.33 (3) -0.56 (4) 0.25 Can be done in a variety of ways. (3) (1) (1)