6.7 D 1 & 2: Inverse & composite inverse trig functions QZ

Find the exact inverse value in radians.

 $\sin^{-1}\left(\frac{\sqrt{3}}{2}\right)$  

•  $\frac{\pi}{3}$  

•  $\frac{\pi}{4}$  

•  $\frac{\pi}{6}$  

•  $\frac{\pi}{2}$  

Find the exact inverse value in radians.

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

•  $\frac{\pi}{3}$  

•  $\frac{\pi}{4}$  

•  $\frac{\pi}{6}$  

•  $\frac{\pi}{2}$  

Find the exact inverse value in radians.

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

•  $\frac{2\pi}{3}$  

•  $\frac{3\pi}{2}$  
  

•  $\frac{3\pi}{4}$  

•  $\frac{5\pi}{6}$  

Find the exact inverse trig value in degrees.

 $\tan^{-1}\left(1\right)$  

• 30 degrees
  

• 45 degrees

• 60 degrees

• 90 degrees

Evaluate the combined expression.

 $\tan\left(\tan^{-1}\left(5.458\right)\right)$  

• All real numbers

• no solution

• 5.458

• -5.458

Evaluate the combined expression.

 $\sin^{-1}\left(\cos\left(\frac{5\pi}{4}\right)\right)$  

•  $-\frac{\pi}{4}$  

•  $\frac{\pi}{4}$  

•  $\frac{3\pi}{4}$  

•  $\frac{7\pi}{4}$  

Evaluate the combined expression.

 $\cos\left(\sin^{-1}\left(-\frac{4}{5}\right)\right)$  

•  $-\frac{5}{4}$  

•  $-\frac{3}{5}$  

•  $\frac{4}{5}$  

•  $\frac{3}{5}$  

Evaluate the combined expression.

 $\cos^{-1}\left(\sin\left(\frac{4\pi}{3}\right)\right)$  

•  $\frac{7\pi}{6}$  

•  $\frac{4\pi}{3}$  

•  $\frac{5\pi}{6}$  

•  $\frac{3\pi}{4}$  

Evaluate the combined expression.

 $\sec\left(\tan^{-1}\left(x\right)\right)$  

• x

•  $\frac{x\sqrt{x^2+1}}{x^2+1}$  

•  $\sqrt{x^2+1}$  

•  $\frac{1}{x}$  

Evaluate the combined expression.

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

•  $\frac{\sqrt{4-x^2}}{2}$  

•  $-\frac{\sqrt{4-x^2}}{4}$  

•  $\frac{\sqrt{2}}{2-x^2}$  

•  $-\frac{\sqrt{2}}{x^2-4}$