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

Find the exact value of each real number y if it exists. Do not use a calculator.

y = csc⁻¹ √2/2

Find the exact value of each expression. cos⁻¹ (-√2/2)

The following equations cannot be solved by algebraic methods. Use a graphing calculator to find all solutions over the interval [0, 6]. Express solutions to four decimal places.

(arctan x)³ ― x + 2 = 0

Find the exact value of each real number y if it exists. Do not use a calculator.

y = sec⁻¹ 1

Evaluate the expression.

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

Solve each equation for exact solutions.

arcsin 2x + arccos x = π/6

In Exercises 1–26, find the exact value of each expression. _ tan⁻¹ √3/3

Solve each equation for x, where x is restricted to the given interval.

y = 1/2 cot 3 x , for x in [0, π/3]

Find the exact value of each real number y if it exists. Do not use a calculator.

y = sin⁻¹ (―1)

Evaluate each expression without using a calculator.

sec (sec⁻¹ 2)

Solve each equation for x.

4/3 arctan x/2 = π

Write each trigonometric expression as an algebraic expression in u, for u > 0.

cos (arcsin u)

Write each trigonometric expression as an algebraic expression in u, for u > 0.

sin (2 sec⁻¹ u/2)