Solving Trigonometric Equations

In which quadrant(s) does inverse sine exist?

• Q1

• Q2

• Q3

• Q4

In which quadrant(s) does inverse cosine exist?

• Q1

• Q2

• Q3

• Q4

In which quadrant(s) does inverse tangent exist?

• Q1

• Q2

• Q3

• Q4

Evaluate $\cos^{-1}\left(-\frac{\sqrt{2}}{2}\right)$ .

•  $\frac{\pi}{4}$  

•  $\frac{3\pi}{4}$ 

•  $-\frac{\pi}{4}$  

•  $\frac{5\pi}{4}$ 

Evaluate $\arcsin\left(-\frac{1}{2}\right)$ .

•  $\frac{\pi}{6}$ 

•  $\frac{5\pi}{6}$ 

•  $-\frac{\pi}{6}$  

•  $\frac{11\pi}{6}$ 

Evaluate  $\tan^{-1}\left(-\frac{\sqrt{3}}{3}\right)$ .

•  $\frac{\pi}{6}$ 

•  $\frac{5\pi}{6}$ 

•  $-\frac{\pi}{6}$ 

•  $-\frac{5\pi}{3}$ 

Solve the equation over it's specific interval.

 $3=2\tan\theta+5$  

•  $0$  

•  $\frac{\pi}{2}$ 
  

•  $\frac{\pi}{4}$  

•  $-\frac{\pi}{4}$  

•  $\frac{3\pi}{4}$  

Solve the equation over it's specific interval.

 $-3-4\cos\theta=-3$  

•  $0$  

•  $\frac{\pi}{2}$ 
  

•  $\pi$  

•  $\frac{3\pi}{2}$  

•  $2\pi$  

Solve the equation over it's specific interval.

 $2-\frac{2}{5}\sin\theta=\frac{10-\sqrt{3}}{5}$  

•  $\frac{\pi}{6}$  

•  $\frac{\pi}{3}$ 
  

•  $\frac{2\pi}{3}$  

•  $\frac{5\pi}{6}$  

•  $-\frac{5\pi}{3}$  

Solve the equation over the interval $\left[0,2\pi\right)$ .

 $-\frac{14}{5}=-3+\frac{1}{5}\cos\theta$