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Analytic Trig Test REVIEW Using Trig Identities Name ____________________________________ Use the fundamental trigonometric identities to determine the simplified form of the expression. 1. cot ßsin ß 2. sin ßsec ß 3. tan ß sin ß 10. If tan 9 , find cot . 40 Factor the expression and use the fundamental identities to simplify. 11. cos2 xsec2 x cos2 x 12. cos2 xsin2 x cos2 x 4. cot ßtan ß Which expression completes the fundamental trigonometric identity? 5. cos x bg 6. cot b xg 7. csc b xg 8. Is the given a trig identity? 1 [A] secu cosu [B] sin u sinu 2 2 [C] tan ucot 2 u1 1 [D] secusin u 2 [E] tan ucot 2 u1 [F] sin u sinu 2 1 [G] secu cosu sinu [H] cotu cosu Let be an acute angle. Use the given function value and trigonometric identities to find the indicated trigonometric function. 8 9. If sin , find csc . 17 F IJ G H K F I G H J K Convert all of the terms to sines and cosines and simplify to find the expression that completes the identity. tan x 13. sec x 14. secx tanxcscx 15. tan x csc x Add or subtract the fractions. Then simplify using the Pythagorean identities and factoring to find the expression that completes the identity. 1 sinx cosx 16. cosx 1 sinx 17. sinx cosx 1 cosx 1 sinx 18. cot x csc x 1 cscx 1 cotx Verify the identity. cscx csc x 19. 2 secx secx tanx secx tan x 20. sin x sec x tan x 1sin 2 x Show that the equation is an identity. 1secu tanu 21. 2cotu tanu 1secu 22. 1cosu sinu 2cscu sinu 1cosu 23. cos x 1 sinx 1 sin x cos x Identify the x-values that are solutions of the equation. 24. 5 3tanx 3 8 3tanx 25. 3tanx 2 5tanx Find the expression that completes the identity. F I xJ G H4 K 3 I 37. sin F xJ G H4 K 36. cos 38. Find the exact value of the expression. 11 11 cos cos sin sin 12 12 12 12 39. Find the exact value of cos 2x using the double angle formula. 2 cos x , x 13 2 40. Find the exact solutions to the equation in the interval 0, 2 . 2sin 4 x 2cos 2 x 26. 9tanx 8 3 17tanx g 27. 2tanx 7 3 9tanx Use the figures to find the exact value of the trigonometric function. 41. 24 tan 2 28. 3cot 2 x 9 0 Find all solutions of the equation in the interval 0, 2 . g 45 29. 2cosxsinx sinx 0 30. tan 2 6 3 sec 6 2 8 31. 2cot 2 x3 cscx 0 32. 2csc3x 42. cot Use the power-reducing formulas to find the exact value of the trigonometric function. 4 30 3 42. sin 2 15 x 5 33. 5sin 30 2 2 x x 34. 2 sec 2 3 sec 2 0 2 2 43. Express sin9 x sin7 x as a product containing only sines and/or cosines. b g 35. Find the exact value of cos 285 .