Chapter 2: Inverse Trigonometric Functions

1. Find the principal value of $sin^{-1}{-\frac{1}{2}}$.

Solution: $\begin{aligned} & \int \frac{d x}{x^2 \pm a^2}, \int \frac{d x}{\sqrt{x^2 \pm a^2}}, \int \frac{d x}{\sqrt{a^2-x^2}}, \int \frac{d x}{a x^2+b x+c}, \int \frac{d x}{\sqrt{a x^2+b x+c}}, \int \frac{p x+q}{a x^2+b x+c} d x \\ & \int \frac{p x+q}{\sqrt{a x^2+b x+c}} d x, \int \sqrt{a^2 \pm x^2} d x, \int \sqrt{x^2-a^2} d x, \int \sqrt{a x^2+b x+c} d x\end{aligned}$