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Solving a Trigonometric Equation Find the general solution of the equation. 1. 2cos x 1 2 2 2 1 cos x 2 2 cos x 2 2 2 x cos 2 1 3 x , 4 4 n x 4 2 4 4 4 4 4 Solving a Trigonometric Equation Find the general solution of the equation. 2. 7tan x 9 2 7tan x 7 7 7 tan x 1 x tan 1 1 3 7 x , 4 4 3 n x 4 4 4 2 4 4 Solving a Trigonometric Equation Find the general solution of the equation. 5 x , 3. cot x 1 2 6 6 2 cot x 3 5 , n x n cot x 3 6 6 3 tan x 3 6 6 6 3 1 x tan 6 6 3 2 Solving a Trigonometric Equation Find the general solution of the equation. 4. 2cos x 3 2 2 3 cos x 2 11 x , 6 6 11 2n x 2n , 6 6 3 x cos 2 1 2 6 6 6 Solving a Trigonometric Equation Find the general solution of the equation. 5. cot x 1 0 cot x 1 tan x 1 x tan 1 1 3 7 x , 4 4 3 n x 4 4 4 2 4 4 Solving a Trigonometric Equation Find the general solution of the equation. 6. 4sin x 3 0 2 4 sin x 3 4 4 3 2 sin x x 2 3 x sin 2 1 , 3 3 2 n x n , 3 3 4 3 sin x 2 2 3 3 3 3 3 Factoring to Solve a Trigonometric Equation Solve the equation in the interval 0 < x < 2. 7. sin x sin x 0 2 sin x sin x 1 0 sin x 0 sin x 1 x 0 , x 2 Factoring to Solve a Trigonometric Equation Solve the equation in the interval 0 < x < 2. 8. 3 sinx 2 sin x cos x 3 sinx 2 sin x cos x 0 sin x 3 2 cos x 0 2 cos x 3 3 sin x 0 cos x 2 11 x 0 , x 6 , 6 2 6 6 6 Factoring to Solve a Trigonometric Equation Solve the equation in the interval 0 < x < 2. 9. cosx 1sinx 1 0 cos x 1 x0 sin x 1 x 2 Factoring to Solve a Trigonometric Equation Solve the equation in the interval 0 < x < 2. 10. tan x sec x 2 tan x tan x sec x 2 tan x 0 tan xsec x 2 0 sec x 2 2 tan x 0 cos x 2 7 , x0 x 4 , 4 2 4 4 4 Factoring to Solve a Trigonometric Equation Solve the equation in the interval 0 < x < 2. 11. sin x tan x sin x sin x tan x sin x 0 sin x tan x 1 0 sin x 0 tan x 1 5 x 0 , x , 4 4 4 4 4 Factoring to Solve a Trigonometric Equation Solve the equation in the interval 0 < x < 2. 12. tan x tan x 0 2 tan x 1 tan x 0 tan x 0 tan x 1 3 7 x 0 , x 4 , 4 4 2 4 4 4 Using the Quadratic Formula Solve the equation in the interval 0 < x < . 13. 2sin x sin x 3 0 2 2 sin x 3sin x 1 0 2 sin x 3 sin x 1 3 x sin x 2 2 Using the Quadratic Formula Solve the equation in the interval 0 < x < . 14. 2 tan x 3 tan x 1 0 2 9 4 2 1 3 tan x 4 3 9 8 3 17 1.781 tan x 0.281 4 4 1 1 x tan 1.781 x tan 0.281 0.274 0.274 x 2.87 x 1.06 Using the Quadratic Formula Solve the equation in the interval 0 < x < . 15. 5cos x 3cos x 2 2 5 cos x 3cos x 2 0 2 9 4 5 2 3 cos x 10 3 9 40 3 49 0.4 cos x 1 10 10 1 1 x cos 1 x cos 0.4 x 1.16 x Using the Quadratic Formula Solve the equation in the interval 0 < x < . 16. cos x 4 cos x 2 2 cos x 4 cos x 2 0 2 4 16 4 1 2 cos x 2 4 16 8 4 8 3.414 cos x 0.586 2 2 1 x cos 0.586 x 0.945