Solving Trig Equations

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

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

•  $\frac{7\pi}{6}$  

•  $\frac{3\pi}{2}$  

•  $\frac{11\pi}{6}$  

•  $\frac{\pi}{3}$  

•  $\frac{5\pi}{6}$  

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

 $\sqrt{2}\cos\theta=-\sin2\theta$  

•  $\frac{\pi}{2}$  

•  $\frac{5\pi}{4}$  

•  $\frac{3\pi}{2}$  

•  $\frac{7\pi}{4}$  

• No Solutions

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

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

•  $\frac{\pi}{4}$  

•  $\frac{3\pi}{4}$  

•  $\frac{5\pi}{4}$  

•  $\frac{7\pi}{4}$  

• No Solutions

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

 $4\sec\theta-5=\sec^2\theta-1$  

•  $\frac{\pi}{3}$  

•  $\frac{5\pi}{3}$  

•  $\frac{\pi}{6}$  

•  $\frac{11\pi}{6}$  

•  $\pi$  

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

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

•  $\frac{\pi}{2}$  

•  $\frac{11\pi}{6}$  

•  $\frac{4\pi}{3}$  

•  $0$  

• no solution

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

 $-2\sqrt{2}=4\sin3\theta$  

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

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

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

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

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

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

•  $\frac{2\pi}{3}$  

•  $\pi$  

•  $\frac{4\pi}{3}$  

•  $\frac{5\pi}{3}$  

•  $\frac{\pi}{3}$  

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

 $3=-\tan^2\theta-3\sec\theta$  

•  $\frac{2\pi}{3}$  

•  $\pi$  

•  $\frac{4\pi}{3}$  

•  $0$  

•  $\frac{\pi}{2}$  

Tags

CCSS.HSF.TF.B.7

Find all solutions to the equation.

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

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

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

• No Solution

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

Tags

CCSS.HSF.TF.B.7

Find all the solutions to the equation.

 $5-2\sin\theta=6$  

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

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

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

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

Tags

CCSS.HSF.TF.B.7