Trig 3.1

Trig 3.1

Inverse Trigonometric Functions

Multiple Choice

Quick Check 1
Find the exact value of $\sin^{-1}\left(1\right)$ . 

•  $0$  

•  $\frac{\pi}{2}$  

•  $-\frac{\pi}{2}$  

•  $\frac{\sqrt{3}}{2}$  

Multiple Choice

Quick Check 2
Find the exact value of

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

•  $\frac{\pi}{6}$  

•  $\frac{5\pi}{6}$  

•  $\frac{3\pi}{4}$  

•  $-\frac{\pi}{4}$  

Multiple Choice

Quick Check 3
Find the exact value of $\tan^{-1}\left(-\sqrt{3}\right)$  

•  $-\frac{\pi}{3}$  

•  $\frac{1}{2}$  

• 0

• Undefined

Multiple Choice

Quick Check 5

Can I estimate the value of  $\cos^{-1}\left(4.23\right)$ ? Why or why not? 

• Yes! The domain of  $\cos^{-1}$ is  $\left(-\infty,\infty\right)$   

• No. We need to convert 4.23 to radians first.

• Yes! Since cosine is one-to-one, I should be able to find the inverse at any value.

• No. The domain of  $\cos^{-1}$  is  $\left[-1,1\right]$  

Multiple Choice

Quick Check 6
Find the exact value of  $\cos\left(\cos^{-1}\left(1.5\right)\right)\$ if it exists. 

• 1.5

• Does Not Exist 

Multiple Choice

Solve the equation:  $3\sin^{-1}x=\pi$  

Hint: Get the trig term by itself then use inverse properties! 

•  $\frac{\pi}{3}$  

•  $\frac{\sqrt{3}}{2}$  

• No solution

• -1