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INSTRUCTOR: Dr. Bathi Kasturiarachi NAME: Math 11022 Fall 2008 Trigonometry REVIEW for Exam 2 { Sections (6.5, 7.1, 7.2, 7.3) 1. Find the exact value of arcsin(1) 2. Find the exact value of tan 5 4 tan sin 1 1 2 tan cos 1 2 5 tan 3. 4. 5. 1 Find the exact value of Find the exact value of Find an algebraic expression in terms of x for the following. sin (arccos x) 6. Find an algebraic expression in terms of x for the following. ! p x2 5 1 sec cos 2x 7. Prove the following trigonometric identity. 1 8. 1 1 + cos x 1 + cos x Prove the following trigonometric identity. sin3 + cos3 9. (sin + cos )(1 Prove the following trigonometric identity. tan2 x sec x + 1 10. 2 csc2 x 1 cos x cos x Prove the following trigonometric identity. (tan 11. Find exact value of sin(195o ). 12. Find exact value of cos(17 =12). sec )2 1 1 sin 1 + sin sin cos ) 13. If sin = 1 5 nd the exact values of the following. sin( 14. =4) cos( Find the exact value of sin sin =3) 4 5 1 tan tan( + =6) 1 15. Find the exact value of the expression: sin 105o 16. Find the exact value of the expression: sin 17. For the angles 18. If sin = 19. If sin = 4 5 3 7 and and and 5 12 shown in the gures, nd cos( + ). lies in quadrant III, nd sin( =2). lies in quadrant II, nd cos( =2). 2 3 4 20. Find the exact value of sin(2x), if cos x = 2 3 and 0o < x < 90o . 21. Find the exact value of cos(2x), if tan x = 5 4 and x lies in quadrant III. 22. Verify the identity: 23. sin 4 4 sin( ) cos( ) cos(2 ) cos 4x 8 cos4 x Verify the identity: 3 8 cos2 x + 1 24. Express the following product as a sum. sin 6 sin 4 25. Express the following product as a sum. cos 3 cos 26. Express the following sum as a product. sin 5 27. sin 3 Express the following sum as a product. cos 3 + cos 2 28. Prove the identity: sin 4x + sin 8x sin 4x sin 8x 4 tan 6x cot(2x)