5. Inverse Trigonometric Functions and Basic Trigonometric Equations

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)

Evaluate each expression without using a calculator.

tan⁻¹ (tan (π/4))

Solve each equation for exact solutions.

6 sin⁻¹ x = 5π

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

y = csc⁻¹ (―2)

Evaluate each expression without using a calculator.

sin (arccos (3/4))

Which one of the following equations has solution 3π/4

a. arctan 1 = x

b. arcsin √2/2 = x

c. arccos (―√2 /2) = x

Solve each equation for exact solutions.

cos⁻¹ x = sin⁻¹ 3/5

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

y = arcsec (2√3)/3

Evaluate each expression without using a calculator.

cos (csc⁻¹ (-2))

Solve each equation for exact solutions.

tan⁻¹ x = cot⁻¹ 7/5