5. Inverse Trigonometric Functions and Basic Trigonometric Equations

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

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

y = cos⁻¹ (―0.32647891)

Solve each equation for x.

y = 1/2 tan (3x + 2), for x in [-2/3 - π/6, -2/3 + π/6]

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

y = arctan 1.1111111

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

y = cot⁻¹ (―0.92170128)

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

y = sec⁻¹ (―1.2871684)

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

y = 5 cos x , for x in [0, π]