5. Inverse Trigonometric Functions and Basic Trigonometric Equations

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

sin (2 sec⁻¹ u/2)

Find the exact value of each expression. cos⁻¹ √3/2

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

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

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

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

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

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

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

In Exercises 27–38, use a calculator to find the value of each expression rounded to two decimal places. sin⁻¹ 0.3

In Exercises 27–38, use a calculator to find the value of each expression rounded to two decimal places. sin⁻¹ (-0.32)

In Exercises 29–51, find the exact value of each expression. Do not use a calculator. cos⁻¹ (− 1/2)

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