5. Inverse Trigonometric Functions and Basic Trigonometric Equations

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

y = arctan 0

Use a calculator to approximate each value in decimal degrees.

θ = cot⁻¹ (-0.60724226)

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

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

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

y = arcsec (2√3)/3

Solve each equation for exact solutions.

sin⁻¹ x - tan⁻¹ 1 = -π/4

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

y = sin⁻¹ √2/2

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

sec (arccot (√4―u² )/ u)

Use a calculator to approximate each real number value. (Be sure the calculator is in radian mode.) 

y = cot⁻¹ (―0.92170128)

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

y = cot⁻¹ (―1)

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

y = 3 tan 2x , for x in [―π/4, π/4]

Evaluate each expression without using a calculator.

sin (2 cos⁻¹ (1/5))

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

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

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

Use a calculator to approximate each value in decimal degrees.

θ = arccos (-0.39876459)

In Exercises 29–51, find the exact value of each expression. Do not use a calculator. tan [cos⁻¹ (− 4/5)]