Exercise 4D

### Write down the interval for the principal-value branch of each of the following functions and draw its graph:

Solution: Principal value branch of $\operatorname{cosec}^{-1} x$ is $\left[-\frac{\pi}{2}, 0\right) \cup\left(0, \frac{\pi}{2}\right]$

### Write down the interval for the principal-value branch of each of the following functions and draw its graph:

Solution: Principal value branch of $\sec ^{-1} x$ is $\left[0, \frac{\pi}{2}\right) \cup\left(\frac{\pi}{2}, \pi\right]$

### Write down the interval for the principal-value branch of each of the following functions and draw its graph:

Solution: Principal value branch of $\cot ^{-1} x$ is $(0, \pi)$

### Write down the interval for the principal-value branch of each of the following functions and draw its graph:

Solution: Principal value branch of $\tan ^{-1} \times$ is $\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$

Solution: Principal value branch of $\cos ^{-1} x$ is $[0, \pi]$
Solution: Principal value branch of $\sin ^{-1} x$ is $\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$