Math Analysis Honors – Worksheet 106 Solving Trigonometric Equations Find all solutions of the equation in the interval 0, 2 algebraically. 1. csc2 x 2 0 2. 2sin2 x 2 cos x 3. sec2 x sec x 2 4. sec x csc x 2 csc x 5. 2sin x csc x 0 6. sec x tan x 1 7. cos x sin x tan x 2 8. cos 2x 2 cos x 1 0 9. 4 sin2 x 4 cos x 1 Use a graphing calculator to graph function (a) f x and approximate the x-coordinate of the maximum and minimum points of the graph in the interval 0, 2 . Solve the trigonometric equation (b) in the interval 0, 2 algebraically. Explain what you notice. 10. (a) f x sin 2x 11. (a) f x sin2 x cos x (b) 2 cos 2x 0 (b) 2sin x cos x sin x 0 12. (a) f x sin x cos x (b) cos x sin x 0 13. (a) f x 2sin x cos 2x (b) 2cos x 4 sin x cos x 0 Math Analysis Honors – Worksheet 94 Solving Trigonometric Equations Find all solutions of the equation in the interval 0, 2 algebraically. 1. csc2 x 2 0 2. 2sin2 x 2 cos x 3. sec2 x sec x 2 4. sec x csc x 2 csc x 5. 2sin x csc x 0 6. sec x tan x 1 7. cos x sin x tan x 2 8. cos 2x 2 cos x 1 0 9. 4 sin2 x 4 cos x 1 Use a graphing calculator to graph function (a) f x and approximate the x-coordinate of the maximum and minimum points of the graph in the interval 0, 2 . Solve the trigonometric equation (b) in the interval 0, 2 algebraically. Explain what you notice. 10. (a) f x sin 2x 11. (a) f x sin2 x cos x (b) 2 cos 2x 0 (b) 2sin x cos x sin x 0 12. (a) f x sin x cos x (b) cos x sin x 0 13. (a) f x 2sin x cos 2x (b) 2cos x 4 sin x cos x 0
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