Evaluating inverse trigonometric functions

In this lesson, we will learn:

• Application of the Cancellation Laws
• Solving Expressions With One Inverse Trigonometry
• Evaluating Expressions With a Combination of Inverse and Non-Inverse Trigonometry
• Special Cases: Evaluating Functions With Numbers Outside of the Restrictions

Cancellation Laws:

$\sin^{-1} (\sin x) = x\;$, $-\frac{\pi}{2} \leq x \leq \frac{\pi}{2}$

$\sin (\sin^{-1} x) = x\;$, $-1 \leq x \leq 1$

$\cos^{-1} (\cos x) = x\;$, $0 \leq x \leq \pi$

$\cos (\cos^{-1} x) = x\;$, $-1 \leq x \leq 1$

$\tan^{-1} (\tan x) = x\;$, $-\frac{\pi}{2} \leq x \leq \frac{\pi}{2}$

$\tan (\tan^{-1} x) = x\;$, $-\infty$ < $x$ < $\infty$

Trigonometric Identity:

$\cos 2\theta = \cos^{2} \theta - \sin^{2} \theta$