5. Inverse Trigonometric Functions and Basic Trigonometric Equations

Evaluate the expression using a calculator. Express your answer in radians, rounding to two decimal places.

$\(\cos\)^{-1}\(\left\)(\(\frac\)14\(\right\))$

Evaluate the expression using a calculator. Express your answer in radians, rounding to two decimal places.

$\(\tan\)^{-1}\(\left\)(5\(\right\))$

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, $x=arccos\left(\frac{1}{2}\right)$)?

Evaluate the expression.

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

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

Evaluate the expression.

$\(\sin\)^{-1}1$

Evaluate the expression.

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

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.

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

Evaluate the expression.

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

Evaluate the expression.

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

Evaluate the expression.

$\(\tan\)^{-1}1$