5. Inverse Trigonometric Functions and Basic Trigonometric Equations

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

θ = csc⁻¹ (-2)

Solve each equation for exact solutions.

cos⁻¹ x + tan⁻¹ x = π/2

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

θ = sin⁻¹ 2

Use a calculator to approximate each value in decimal degrees.

θ = sin⁻¹ (-0.13349122)

Solve each equation for exact solutions.

tan⁻¹ x - tan⁻¹ (1/x ) = π/6

Which one of the following equations has solution π?

a. arccos (―1) = x

b. arccos 1 = x

c. arcsin (―1) = x

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

y = sin⁻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

Use a calculator to approximate each value in decimal degrees.

θ = arccos (-0.39876459)

Use a calculator to approximate each value in decimal degrees.

θ = csc⁻¹ 1.9422833

Use a calculator to approximate each value in decimal degrees.

θ = cot⁻¹ (-0.60724226)

Solve each equation for x.

4/3 arctan x/2 = π

Solve each equation for x.

arccos x + arctan 1 = 11π/12

Use a calculator to approximate each value in decimal degrees.

θ = tan⁻¹ (-7.7828641)

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

y = arcsin 0.92837781