5. Inverse Trigonometric Functions and Basic Trigonometric Equations

Use a calculator to approximate each value in decimal degrees.

θ = arctan 1.7804675

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

y = 1/2 cot 3 x , for x in [0, π/3]

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 = cos⁻¹ 0.80396577

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

y = cos (x + 3) , for x in [―3, π―3]

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

y = arcsin (―√3/2)

Use a calculator to approximate each value in decimal degrees.

θ = arcsec 3.4723155

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

y = √2 + 3 sec 2x, for x in [0, π/4) ⋃ (π/4, π/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.

cos (arccos (-1))

Solve each equation for exact solutions.

-4 arcsin x = π

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

y = sin⁻¹ √3

Evaluate each expression without using a calculator.

arccos (cos (3π/4))

Solve each equation for exact solutions.

4/3 cos⁻¹ x/4 = π

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

y = cot⁻¹ (―1)