Inverse Trigonometric Functions

Which can be a restriction for the domain of y = sin x so the inverse sine can be a function?

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

• $\left[0,\ \pi\right]$

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

• $\left[0,\ 2\pi\right]$

Tags

CCSS.HSF.BF.B.4

CCSS.HSF.TF.B.6

Which can be a restriction for the domain of y = cos x so the inverse cosine can be a function?

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

• $\left[0,\ \pi\right]$

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

• $\left[0,\ 2\pi\right]$

Tags

CCSS.HSF.BF.B.4

CCSS.HSF.TF.B.6

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

•  $\frac{\pi}{6}$  

•  $\frac{3\pi}{4}$  

•  $\frac{2\pi}{3}$  

•  $\frac{5\pi}{6}$  

Tags

CCSS.HSF.TF.A.1

CCSS.HSF.TF.A.2

CCSS.HSF.TF.A.3

CCSS.HSF.TF.B.7

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

•  $\frac{\pi}{6}$  

•  $\frac{3\pi}{4}$  

•  $\frac{2\pi}{3}$  

•  $\frac{5\pi}{6}$  

Tags

CCSS.HSF.TF.A.3

CCSS.HSF.TF.B.7

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

•  $\frac{\pi}{6}$  

•  $-\frac{\pi}{4}$  
  

•  $\frac{\pi}{4}$  
  

•  $\frac{\pi}{3}$  
  

Tags

CCSS.HSF.TF.A.3

CCSS.HSF.TF.B.7

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

•  $\frac{\pi}{6}$  

•  $-\frac{\pi}{4}$  
  

•  $\frac{\pi}{4}$  
  

•  $-\frac{\pi}{6}$  
  

Tags

CCSS.HSF.TF.A.3

CCSS.HSF.TF.B.7

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

•  $\frac{\sqrt{3}}{2}$  
  

•  $\frac{\sqrt{2}}{2}$  
  

•  $-\frac{\sqrt{3}}{2}$  
  

•  $-\frac{\sqrt{2}}{2}$  
  

Tags

CCSS.HSF.TF.A.3

CCSS.HSG.SRT.C.6

CCSS.HSG.SRT.C.8

Find the exact value of $\cos^{-1}\left(\tan\ \frac{\pi}{4}\right)$ . 

•  $\frac{\sqrt{2}}{2}$  
  

• 1

• 0

•  $-\frac{\sqrt{2}}{2}$  
  

Tags

CCSS.HSF.TF.A.3

CCSS.HSF.TF.B.7

Find the exact value of $\tan^{-1}\left(\tan\ \frac{3\pi}{4}\right)$ . 

•  $\frac{\pi}{4}$  
  

•  $-\frac{\pi}{4}$  
  

•  $-\frac{\pi}{3}$  
  

•  $\frac{\pi}{6}$  
  

Tags

CCSS.HSF.TF.A.3

CCSS.HSF.TF.B.7

Tags

CCSS.HSF.TF.A.1

CCSS.HSF.TF.A.2

CCSS.HSF.TF.A.3

CCSS.HSF.TF.B.7