5. Inverse Trigonometric Functions and Basic Trigonometric Equations

Given a right triangle where the length of the adjacent side to angle $x$ is $1$ and the hypotenuse is $2$, in which triangle is the value of $x$ equal to ${cos}^{-1}\left(1,/,2\right)$ (that is, $x=arccos\left(\frac{1}{2}\right)$)?

For which interval of $x$ is the cancellation property ${\sin }^{-1}\left(\sin \right(x\left)\right)=x$ valid?

Given the function $y=cot\left(x\right)$, which of the following statements is true about its inverse function $y=arccot\left(x\right)$?

Evaluate the expression.

$\cos^{-1}\left(-1\right)$

Evaluate the expression.

$\cos^{-1}\left(0\right)$

Evaluate the expression.

$\cos^{-1}\left(-\frac{\sqrt2}{2}\right)$

Evaluate the expression.

$\sin^{-1}1$

Evaluate the expression.

$\sin^{-1}\left(\frac{\sqrt3}{2}\right)$

Evaluate the expression.

$\sin^{-1}\left(\frac{\sqrt2}{2}\right)$

Evaluate the expression.

$\tan^{-1}0$

Evaluate the expression.

$\tan^{-1}1$

Evaluate the expression.

$\tan^{-1}\left(-\frac{\sqrt3}{3}\right)$