# 9.5E: Solving Trigonometric Equations (Exercises)

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For the following exercises, find all exact solutions on the interval $$[0,2 \pi)$$.

39. $$\tan x+1=0$$

40. $$2 \sin (2 x)+\sqrt{2}=0$$

For the following exercises, find all exact solutions on the interval $$[0,2 \pi)$$.

41. $$2 \sin ^{2} x-\sin x=0$$

42. $$\cos ^{2} x-\cos x-1=0$$

43. $$2 \sin ^{2} x+5 \sin x+3=0$$

44. $$\cos x-5 \sin (2 x)=0$$

45. $$\frac{1}{\sec ^{2} x}+2+\sin ^{2} x+4 \cos ^{2} x=0$$

For the following exercises, simplify the equation algebraically as much as possible. Then use a calculator to find the solutions on the interval $$[0,2 \pi)$$. Round to four decimal places.

46. $$\sqrt{3} \cot ^{2} x+\cot x=1$$

47. $$\csc ^{2} x-3 \csc x-4=0$$

For the following exercises, graph each side of the equation to find the approximate solutions on the interval $$[0,2 \pi)$$.

48. $$20 \cos ^{2} x+21 \cos x+1=0$$

49. $$\sec ^{2} x-2$$ sec $$x=15$$

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