5. Inverse Trigonometric Functions and Basic Trigonometric Equations

Solve each equation for exact solutions.

6 sin⁻¹ x = 5π

Solve each equation for exact solutions.

2 arccos (x/3 - π/3) = 2π

Give the degree measure of θ. Do not use a calculator.

θ = arcsin (―√3/2)

Solve each equation for exact solutions.

tan⁻¹ x = cot⁻¹ 7/5

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

θ = arctan (-1)

In Exercises 39–54, find the exact value of each expression, if possible. Do not use a calculator. tan⁻¹ [tan(− π/6)]

In Exercises 29–51, find the exact value of each expression. Do not use a calculator. _ sin⁻¹ (− √3/2)

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

y = sec⁻¹ (―2)

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

y = arccos (―√3/2)

Evaluate each expression without using a calculator.

sin (sin⁻¹ 1/2 + tan⁻¹ (-3))

In Exercises 29–51, find the exact value of each expression. Do not use a calculator. sin(cos⁻¹ 3/5)

Use a calculator to approximate each value in decimal degrees.

θ = csc⁻¹ 1.9422833

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

cos (tan⁻¹ 0.5)

The graphs of y = sin⁻¹ x, y = cos⁻¹ x, and y = tan⁻¹ x are shown in Table 2.8. In Exercises 97–106, use transformations (vertical shifts, horizontal shifts, reflections, stretching, or shrinking) of these graphs to graph each function. Then use interval notation to give the function's domain and range. h(x) = −2 tan⁻¹ x