Free Printable Solving Trig Equations

1.

$0=4\sin^2\theta+\cos2\theta+3\sin\theta$

Solve the equation. Restrict your answer to [0,2π).

a)

$\frac{7\pi}{6}$

b)

$\frac{3\pi}{2}$

c)

$\frac{11\pi}{6}$

d)

$\frac{\pi}{3}$

e)

$\frac{5\pi}{6}$

2.

Solve the equation. Restrict your answer to [0,2π).

$\sqrt{2}\cos\theta=-\sin2\theta$

a)

$\frac{\pi}{2}$

b)

$\frac{5\pi}{4}$

c)

$\frac{3\pi}{2}$

d)

$\frac{7\pi}{4}$

e)

No Solutions

3.

Solve the equation. Restrict your answer to [0,2π).

$-2\sec\theta=\sqrt{2}\tan\theta-3\sec\theta$

a)

$\frac{\pi}{4}$

b)

$\frac{3\pi}{4}$

c)

$\frac{5\pi}{4}$

d)

$\frac{7\pi}{4}$

e)

No Solutions

4.

Solve the equation. Restrict your answer to [0,2π).

$4\sec\theta-5=\sec^2\theta-1$

a)

$\frac{\pi}{3}$

b)

$\frac{5\pi}{3}$

c)

$\frac{\pi}{6}$

d)

$\frac{11\pi}{6}$

e)

$\pi$

5.

Solve the equation. Restrict your answer to [0,2π).

$4+\csc\left(\theta+\frac{\pi}{3}\right)=6$

a)

$\frac{\pi}{2}$

b)

$\frac{11\pi}{6}$

c)

$\frac{4\pi}{3}$

d)

$0$

e)

no solution

6.

Solve the equation. Restrict your answer to [0,2π).

$-2\sqrt{2}=4\sin3\theta$

a)

$\left\{\frac{\pi}{24},\frac{13\pi}{24},\frac{7\pi}{12},\frac{25\pi}{24},\frac{29\pi}{24},\frac{5\pi}{4},\frac{7\pi}{4}\right\}$

b)

$\left\{\frac{7\pi}{12},\frac{25\pi}{24},\frac{13\pi}{12},\frac{7\pi}{4},\frac{23\pi}{12}\right\}$

c)

$\left\{\frac{25\pi}{24},\frac{41\pi}{24},\frac{7\pi}{4}\right\}$

d)

$\left\{\frac{5\pi}{12},\frac{7\pi}{12},\frac{13\pi}{12},\frac{5\pi}{4},\frac{7\pi}{4},\frac{23\pi}{12}\right\}$

7.

Solve the equation. Restrict your answer to [0,2π).

$5\cos^2\theta=-1-3\cos\theta+3\cos^2\theta$

a)

$\frac{2\pi}{3}$

b)

$\pi$

c)

$\frac{4\pi}{3}$

d)

$\frac{5\pi}{3}$

e)

$\frac{\pi}{3}$

8.

Solve the equation. Restrict your answer to [0,2π).

$3=-\tan^2\theta-3\sec\theta$

a)

$\frac{2\pi}{3}$

b)

$\pi$

c)

$\frac{4\pi}{3}$

d)

$0$

e)

$\frac{\pi}{2}$

9.

Find all solutions to the equation.

$6\cos\left(\theta+\pi\right)=-3\sqrt{3}$

a)

$\left\{\frac{\pi}{6}+2\pi n\right\}$

b)

$\left\{-\frac{\pi}{6}+2\pi n,\frac{\pi}{6}+2\pi n\right\}$

c)

No Solution

d)

$\left\{4\pi+6\pi n,2\pi+6\pi n,-\frac{\pi}{6}+2\pi n,\frac{\pi}{6}+2\pi n\right\}$

10.

Find all the solutions to the equation.

$5-2\sin\theta=6$

a)

$\left\{\frac{7\pi}{6}+2\pi n,\frac{11\pi}{6}+2\pi n\right\}$

b)

$\left\{\frac{7\pi}{6}+2\pi n\right\}$

c)

$\left\{\frac{3\pi}{4}+2\pi n,\ \frac{\pi}{4}+2\pi n,\ \frac{7\pi}{6}+2\pi n\right\}$

d)

$\left\{\frac{3\pi}{4}+2\pi n,\frac{\pi}{4}+2\pi n\right\}$

11.

Find all the solutions to the equation.

$-4\sqrt{3}+3\tan\theta=-\tan\theta$

a)

$\pi n$

b)

$\left\{\frac{7\pi}{4}+\pi n\right\}$

c)

$\left\{\frac{\pi}{3}+\pi n\right\}$

d)

No Solution

12.

Solve the equation. Restrict your answer to [0,2π).

$-2\cos\theta=\cos\theta\sec\theta-3\cos\theta$

a)

$0$

b)

$\pi$

c)

$\frac{\pi}{2}$

d)

$\frac{3\pi}{2}$

e)

No Solution

Solving Trig Equations

Total questions: 12

Worksheet time: 34mins

Similar Resources on Wayground