Inverse Trig Review #1

Which of the following is the graph of  $\sin^{-1}x$  ?

• 
• 
• 
• 

What is the range of  $\cos^{-1}x$  ?

•  $\left(-\infty,\infty\right)$  

•  $-\frac{\pi}{2}\le x\le\frac{\pi}{2}$  

•  $0\le x\le\pi$  

•  $0\le x\le2\pi$  

Which identity allows for this statement to be true?
 $\sin\left(120\degree\right)=\cos\left(30\degree\right)$  

• Sum Identity for Sine

• Pythagorean Identity

• Double Angle Identity

• Co-function identity

Simplify.

• 1

• $\sin\left(x\right)$

• $\sec\left(x\right)$

• $\cos\left(x\right)$

Simplify.

• $\tan^2\left(x\right)$

• $\sin^2\left(x\right)$

• $\csc\left(x\right)$

• $\sin\left(x\right)$

Find the exact value of $\cos\left(2x\right)$  if  $\sin x=-\frac{12}{13}$  and in Quadrant III.

•  $-\frac{5}{13}$  

•  $-\frac{10}{13}$  

•  $\frac{457}{169}$  

•  $-\frac{119}{169}$  

To determine the $\cos\left(75\degree\right)$  , you can use the cosine of a sum identity:

 $\cos\left(45\degree+30\degree\right)=$  

•  $\cos\left(45\degree\right)\cos\left(30\degree\right)+\sin\left(45\degree\right)\sin\left(30\degree\right)$  

•  $\cos\left(45\degree\right)\cos\left(30\degree\right)-\sin\left(45\degree\right)\sin\left(30\degree\right)$  

•  $\cos\left(45\degree\right)\sin\left(30\degree\right)+\cos\left(30\degree\right)\left(\sin45\degree\right)$  

•  $\cos\left(45\degree\right)\sin\left(30\degree\right)-\sin\left(45\degree\right)\cos\left(30\degree\right)$  

 Evaluate: 

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

•  $\frac{7\pi}{6}$  

•  $\frac{11\pi}{6}$  

•  $-\frac{\pi}{6}$  

•  $\frac{2\pi}{3}$  

Evaluate:

 $\sin^{-1}\left(\sin\pi\right)$  

•  $\pi$  

•  $0$  

•  $-\frac{\pi}{2}$  

•  $\frac{\pi}{2}$  

Select ALL correct trig identities:

•  $\sin x+\cos x=1$  

•  $\sin\left(2x\right)=2\sin x\cos x$  

•  $1+\tan^2x=\sec^2x$  

•  $\tan\left(90\degree-\theta\right)=\sec\left(\theta\right)$  

•  $\sin\left(\frac{\theta}{2}\right)=\pm\sqrt{\frac{1-\cos\theta}{2}}$