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.
Understanding the Use of Inverse Trigonometric Functions
Find the angles for each of the following diagrams.

3.
Determining the Angles in Exact Values by Using Special Triangles
Find the angles for each of the following diagrams in exact value.

4.
Application of the Cancellation Laws
Solve the following inverse trigonometric functions:

5.
Solving Expressions With One Inverse Trigonometry
Solve the following inverse trigonometric functions:

6.
Evaluating Expressions With a Combination of Inverse and NonInverse Trigonometry
Solve the following inverse trigonometric functions:

7.
Special Cases: Evaluating Functions With Numbers Outside of the Restrictions
Solve the following inverse trigonometric functions: