Inverse Trigonometric Functions

What test will you use to determine if a function is one-to-one?

• Veetical Line Test

• Horizontal Line Test

• One-to-one Test

• Function Domain-Range Test

Tags

CCSS.HSF.BF.B.4

CCSS.HSF.IF.C.7

Complete the statement:

 $f^{-1}\left(f\left(y\right)\right)=y\ \ for\ every\ y\ in\ the...$  

• domain of  $f$  

• range of  $f$  

• set of real numbers

• domain of  $f^{-1}$  

Find the exact value of  $\cos^{-1}\left(\frac{\sqrt{3}}{2}\right)$  

•  $-\frac{\pi}{3}$  

•  $\frac{\pi}{3}$  

•  $-\frac{\pi}{6}$  

•  $\frac{\pi}{6}$  

Tags

CCSS.HSF.TF.A.3

CCSS.HSF.TF.B.7

What is the domain of the inverse cotangent function?

•  $\left(-\frac{\pi}{2},\frac{\pi}{2}\right)$  

•  $\left[0,\pi\right]$  

•  $\left(-\infty,+\infty\right)$  

•  $\left(-1,1\right)$  

Find the exact value of  $\sec^{-1}\left(-2\right)$  

•  $\frac{2\pi}{3}$  

•  $-\frac{\pi}{3}$  

•  $\frac{4\pi}{3}$  

•  $-\frac{2\pi}{3}$  

Tags

CCSS.HSF.BF.B.4

CCSS.HSF.TF.B.6

CCSS.HSF.TF.B.7

Find the exact value of  $\tan\left(\tan^{-1}\left(\theta\right)\right)\ if\ \theta=2$  

• 2

• Undefined

• Can't be determined

Find the exact value of  $\sec^{-1}\left(\sec\left(\frac{\pi}{2}\right)\right)$  

•  $\frac{\pi}{2}$  

• Undefined

• Can't be determined

Find the exact value of  $\csc^{-1}\left(\frac{2\sqrt{3}}{3}\right)$  

•  $\frac{2\pi}{3}$  

•  $-\frac{\pi}{3}$  

•  $\frac{\pi}{6}$  

•  $\frac{\pi}{3}$  

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

•  $\frac{\pi}{4}$  

•  $\frac{3\pi}{4}$  

•  $-\frac{\pi}{4}$  

•  $\frac{7\pi}{4}$  

What is the restricted domain of the cosine function in order to have an inverse cosine function?

• $\left[0,\pi\right]\ -\ \left\{\frac{\pi}{2}\right\}$

• $\left[0,\pi\right]$

• $\left[-1,1\right]$

• $\left(-\frac{\pi}{2},\frac{\pi}{2}\right)$

Tags

CCSS.HSF.BF.B.4

CCSS.HSF.TF.B.6