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Extension 5.4-5 Including more drill on 5.3 5.3: Solve: [0 x < 2 ) No Calculator. 1. sin x = 3 sin x (2) 3 3 tan x = 3 (3) 3 csc 2 x =4 4. 2cos2x – cos x = 1 (5) cos2x + sin x = 1 (6) 2sin 2x - 7. cos 2x = ½ (8) sec 4x = 2 (9) sin 10. cos 4x(cos x – 1) = 0 (11) tan 2 x tan x 12 0 2 =0 3 x =2 2 5.4: Find the sine, cosine, and tangent of the angle by using a sum or difference formula. 12. 285 (13) 25 12 Write the expression as the sine, cosine, or tangent of an angle. 14. sin 60 cos 45 - cos 60 sin 45 tan 25 tan 10 (15) 1 tan 25 tan 10 Find the exact value of the trigonometric function given that sin u = cos v = 16. 5 . Both u and v are angles in Quadrant II. 13 sin (u + v) (17) cos (u – v) (18) tan (u + v) Verify the Identity: 19. cos(x + ) = - sin x 2 3 and 4 (20) cos 3x= 4 cos 2 x – 3 cos x Solve: [0 x < 2 ) No Calculator. 21. sin (x + ) - sin (x - ) = 1 4 4 (22) cos (x + 3 3 ) - cos (x )= 0 4 4 5.5: Find the exact values of sin 2u, cos 2u and tan 2u using the double angles formulas. 23, sin u = (-4/5) u in Quadrant 3. (24) cos u = 2 u in Quadrant 2. 5 Use double angle formulas to verify the identity. 25. sin 4x = 8 cos 3 x sin x – 4 cos x sin x Use the half angle formulas to determine the exact values of the sine, cosine, and tangent of the angle. 19 26. -75 (27) 12 u u u Find the exact values of sin , cos , tan . 2 2 2 28. sin u = 3 2 , u is in Quadrant I (29) cos u = , u is in Quadrant II 5 7 Simplify with half angle formulas. 30. 1 cos 10 x 2 - Use product to sum formulas to write the product as a sum or difference. 31. cos 6 sin 6 (32) cos 5x cos 3x Use the sum to product formulas to write the sum or difference as a product. 33. sin 4x – sin 2x (34) cos (x + ) - cos (x - ) 6 6