Evaluating inverse trigonometric functions  Inverse Trigonometric Functions
Evaluating inverse trigonometric functions
Basic concepts:
 Quotient identities and reciprocal identities
 Pythagorean identities
 Sum and difference identities
 Cofunction identities
 Doubleangle identities
Related concepts:
 Inverse functions
Lessons
Notes:
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 NonInverse 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:
$\cos 2\theta = \cos^{2} \theta  \sin^{2} \theta$

1.
Application of the Cancellation Laws
Solve the following inverse trigonometric functions:

2.
Solving Expressions With One Inverse Trigonometry
Solve the following inverse trigonometric functions:

3.
Evaluating Expressions With a Combination of Inverse and NonInverse Trigonometry
Solve the following inverse trigonometric functions:

4.
Special Cases: Evaluating Functions With Numbers Outside of the Restrictions
Solve the following inverse trigonometric functions: