INVERSE TRIGONOMETRIC FUNCTIONS

Q1. The principal value of $\ Sin^{-1}\left(\frac{1}{\sqrt{2}}\right)\ is\$  

•  $\frac{\pi}{4}$  

•  $\frac{\pi}{6}$  

•  $\frac{\pi}{2}$  

Q2. The principal value of $\ Sin^{-1}\left(\frac{1}{2}\right)\ is$  

•  $\frac{\pi}{6}$  

•  $-\frac{\pi}{4}$  

•  $-\frac{\pi}{3}$  

Q3. The principal value of $\ Tan^{-1}\left(-1\right)\ is$  

•  $-\frac{\pi}{4}$  

•  $-\frac{\pi}{3}$  

•  $-\frac{\pi}{6}$  

Q4. The principal value branch of $\ \ \left(\ Sin^{-1}y\ \right)\ is\$  

•  $0\le y\le\pi$  

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

•  $-\frac{\pi}{2}<y<\frac{\pi}{2}$  

Q5. The principal value of $\ Cos^{-1}\frac{1}{2}\ +\ 2Sin^{-1}\ \frac{1}{2}\ is$  

•  $\frac{2\pi}{3}$  

•  $\frac{\pi}{4}$  

•  $\frac{2\pi}{6}$  

Q6. The principal value of $\ \ \tan^{-1}\sqrt{3}-\ \sec^{-1}\left(-2\right)\ \ is$  

•  $\pi$  

•  $\frac{\pi}{3}$  

•  $\frac{2\pi}{3}$  

Q7. The principal value of $\ Co\sec^{-1}\left(-\sqrt{2}\right)\ is\$  

•  $-\frac{\pi}{6}$  

•  $-\frac{\pi}{2}$  

•  $-\frac{\pi}{4}$  

Q8. Which of the following is NOT TRUE about inverse functions?

• Inverse functions are reflections of each other over the line y = x.

• You find the inverse by switching x and y in the equation.

• The domain of a function always becomes the domain of its inverse.

• The domain of a function always becomes the range of its inverse.

Q9.  $\cos^{-1}\left(\cos\ \frac{7\pi}{6}\right)\$  is equal to

•  $\frac{7\pi}{6}$  

•  $\frac{5\pi}{6}$  

•  $\frac{-\pi}{3}$  

•  $\frac{-\pi}{6}$  

Q10. Find the principal value of : $\ Cos^{-1}\left\{\tan\ \left(\frac{-\pi}{4}\right)\right\}\$  

• 0

• π

• π/4

• 3π/4