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Chapter 5 Practice Test Name _________________ 1. Graphically determine the general solution: 3sin(5x) = 1 A. x 0.07 2n , x 0.56 2n B. x 0.07 2n , x 5.94 2n 5 5 5 5 C. x 0.07 2n , x 0.56 2n D. x 0.07 2n , x 5.94 2n 2. A. 3. A. 4. A. Graph and solve: sin x +1 = sec x , 0 x 2 0, 1.00 B. 0, 1.84 C. 1.00, 1.84 Solve: 0.52 D. 0, 1.00, 1.57, 4.71 2 sin x cos x 1, where 0 x 2. (Accurate to 2 dec. places.) B. 0.79 C. 0.52, 2.62 D. 0.79, 3.93 Determine the number of solutions for: (tanq + 1)(2sinq + 1)(cosq + 2) = 0, where 0 q < . 2 B. 3 C. 4 D. 6 2 5. How many solutions does sin x A. 1 6. Solve: A. , 2 3 3 B. 2 1 3 have over the interval 0 x 2 ? C. 3 3 2 sin x 0, 0 x 2 (Give exact solutions) B. 4 , 5 C. , 5 3 3 6 6 7. Solve: 4cos2x - 3 = 0 , 0 x 2 A. , 5 , 7 and 11 6 6 6 6 C. , , 3 , and 2 2 2 Give exact solution(s). B. , 2 , 4 and 5 3 3 3 3 D. , 3 , 5 and 7 4 4 4 4 D. 4 D. 7 , 11 6 6 8. Solve : 1 2 sin x 0, 0 x 2 Give exact solution(s). A. B. 2 , 5 C. 2 , D. 7 , 11 6 3 3 3 3 6 6 9. Determine the number of solutions in the interval 0 £ x < 2p for: sinax = 0.5, a is an integer, where a 1 A. 2 B. a 2 C. a 10. A. B. C. D. 11. A. B. C. D. D. 2a 12. A. B. C. D. 13. Which expression below is equivalent to 2 cot A. 2 tan 5 B. 1 2 tan 5 ? 2 C. tan 5 D. 5 2 tan 5 1 2 B. 7 n, 11 n (n is any integer) 12 12 D. 13 n, 21 n (n is any integer) 12 12 14. Determine the general solution for: sin 2 x A. 7 2n, 11 2n (n is any integer) 12 12 C. 13 2n, 21 2n (n is any integer) 12 12 15. Sin( ) equals A. –sin B. sin C. cos 16. What is (are) the restriction(s) for the expression A. sec x 0 B. sin x 0 D. –cos sec x ? sin x C. cos x 0 D. cos x 0, sin x 0 17. For what value of x is the following expression undefined? A. 0 B. 2 C. B. 0, C. 0, 2 sin x , where 0 x 2 1 cos x D. 3 2 18. Determine all values of x for which the following expression is undefined. sin x , 1 sec 2 x where 0 x 2 A. , 3 2 2 19. Simplify: 4 – 8 sin26x. A. cos12x B. 2 cos 6x 20. Determine an expression equivalent to A. csc 2 B. sec 2 C. 4 cos 6x sec 2 . sec 2 2 C. csc 2 D. 0, , , 3 2 2 D. 4 cos 12x D. sec 2 21. Which expression is equivalent to: A. tan tan2 B. 1 tan2 22. Simplify the expression: A. 2 1 tan ? 1 cot C. 1 – cot tan – 1 D. tan C. sin D. sin cos C. cos2q D. cos4q sin2 sin B. 2 cos 23. Simplify : cos4q - sin4q A. –1 B. - cos2q 24. A. sin x B. -sin x C. cos x D. -cos x 25. A. B. C. D. 26. Which expression is equivalent to sin(180º + q)? A. sin q B. –sin q C. cos q D. –cos q 27. Which of the following is equivalent to cos5 cos -sin 5 sin ? A. cos 4 B. cos6 C. cos 4 sin 4 D. cos 6 sin 6 28. Simplify: cos(p – 2x) A. –cos 2x B. –sin 2x C. cos 2x D. sin 2x 3 4 29. If cos A 5 , A in the fourth quadrant, and cos B 5 , B in the first quadrant, then sin (A + B) equals A. 7 25 B. 0 C. 30. Which expression is equivalent to A. cos2(4x) 2 31. Solve sin B. sin2(4x) 1 2 7 25 cos(8 x ) 1 ? 2 C. cos2(16x) D. 1 D. sin2(16x) for to 2 decimal places where 0 2 32. Consider the equation: a. b. Give the general solution for this equation. (Solve over the set of real numbers giving exact value solutions.) 33. 2 34. Solve cos x cos x over the set of real numbers. Give exact value solutions. 35. Give all solutions to: 2cos3x + 36. Prove the following identity: 3=0 1+ cot cot 1+ tan over 0 x 2 (3 marks) (3 marks) Pr ove that 2 csc 2 37. 1 1 1 cos 1 – cos 38. Prove the following identity. sin tan tan 1 cos (2 marks) 2 39. Prove the following identity: 2 – 4 sin 2 cos 2 40. Prove the following identity: csc 2 x 1 sec x csc x 2 41. Prove algebraically the following identity: sin 2 x cot x 1 cos 2 x (2 marks) 42. 43.