5. Inverse Trigonometric Functions and Basic Trigonometric Equations

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

y = tan⁻¹ (―√3)

Graph each inverse circular function by hand.

y = arcsec [(1/2)x]

Evaluate each expression without using a calculator.

tan (arccos 3/4)

Evaluate each expression without using a calculator.

cos (tan⁻¹ (-2))

Evaluate each expression without using a calculator.

sin (2 tan⁻¹ (12/5))

Evaluate each expression without using a calculator.

cos (2 arctan (4/3))

Evaluate each expression without using a calculator.

sin (2 cos⁻¹ (1/5))

Evaluate each expression without using a calculator.

sec (sec⁻¹ 2)

Evaluate each expression without using a calculator.

cos (tan⁻¹ (5/12) - tan⁻¹ (3/4))

Evaluate each expression without using a calculator.

sin (sin⁻¹ 1/2 + tan⁻¹ (-3))

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

y = 3 tan 2x , for x in [―π/4, π/4]

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

y = cos⁻¹ (―√2/2)

Use a calculator to find each value. Give answers as real numbers.

cos (tan⁻¹ 0.5)

Use a calculator to find each value. Give answers as real numbers.

tan (arcsin 0.12251014)

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

sin (arccos u)