5. Inverse Trigonometric Functions and Basic Trigonometric Equations

In Exercises 1–26, find the exact value of each expression. _ csc⁻¹ (− 2√3/3)

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

tan (arcsec (√1―u²) / u)

Find the degree measure of θ if it exists. Do not use a calculator.

θ = arcsin (-√3/2)

Evaluate the expression.

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

In Exercises 27–38, use a calculator to find the value of each expression rounded to two decimal places. tan⁻¹ (−20)

In Exercises 27–38, use a calculator to find the value of each expression rounded to two decimal places. _ cos⁻¹ √5/7

In Exercises 83–94, use a right triangle to write each expression as an algebraic expression. Assume that x is positive and that the given inverse trigonometric function is defined for the expression in x. ___ sec (sin⁻¹ x/√x²+4)

Find the exact value of each expression. sin⁻¹ √2/2

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

tan (sin⁻¹ u/(√u² + 2))

Find the degree measure of θ if it exists. Do not use a calculator.

θ = sin⁻¹ 2

Solve each equation for exact solutions.

arcsin x = arctan 3/4

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

y = arcsin (―√3/2)

Evaluate the expression.

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

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

$\(\sin\)^{-1}\(\left\)(-\(\frac\)13\(\right\))$

Solve each equation for exact solutions.

tan⁻¹ x - tan⁻¹ (1/x ) = π/6