Home fsc 1st year math solutions Solutions of trigonometric solutions|Exercise 14

Solutions of trigonometric solutions|Exercise 14

Trigonometric Identities 10.4
Trigonometric Identities 10.4

Find the solutions of the following equations which lie in [0,2 \pi]
i) \sin x=-\frac{\sqrt{3}}{2}
ii) \operatorname{cosec} \theta=2
iii) \sec x=-2
Solve the following trigonometric equations:
iv) \cot \theta=\frac{1}{\sqrt{3}}
i) \tan ^2 \theta=\frac{1}{3}
ii) \operatorname{cosec}^2 \theta=\frac{4}{3}
iii) \sec ^2 \theta=\frac{4}{3} \quad iv) \cot ^2 \theta=\frac{1}{3}

Find the values of \theta satisfying the following equations:
3. 3 \tan ^2 \theta+2 \sqrt{3} \tan \theta+1=0
4. \tan ^2 \theta-\sec \theta-1=0
5. 2 \sin \theta+\cos ^2 \theta-1=0
6. 2 \sin ^2 \theta-\sin \theta=0
7. 3 \cos ^2 \theta-2 \sqrt{3} \sin \theta \cos \theta-3 \sin ^2 \theta=0 [Hint: Divide by \sin ^2 \theta ]
8. 4 \sin ^2 \theta-8 \cos \theta+1=0

Find the solution sets of the following equations:

  1. \sqrt{3} \tan x-\sec x-1=0
  2. \cos 2 x=\sin 3 x
    [Hint: \sin 3 x=3 \sin x-4 \sin ^3 x ]
  3. \sec 3 \theta=\sec \theta
  4. \tan 2 \theta+\cot \theta=0
  5. \sin 2 x+\sin x=0
  6. \sin 4 x-\sin 2 x=\cos 3 x
  7. \sin x+\cos 3 x=\cos 5 x
  8. \sin 3 x+\sin 2 x+\sin x=0
  9. \sin 7 x-\sin x=\sin 3 x
  10. \sin x+\sin 3 x+\sin 5 x=0
  11. \sin \theta+\sin 3 \theta+\sin 5 \theta+\sin 7 \theta=0
  12. \cos \theta+\cos 3 \theta+\cos 5 \theta+\cos 7 \theta=0
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