5. Inverse Trigonometric Functions and Basic Trigonometric Equations

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

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

y = sec⁻¹ 1

Evaluate each expression without using a calculator.

tan (arcsin (3/5) + arccos (5/7))

Solve each equation for exact solutions.

arcsin x = arctan 3/4

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

y = csc⁻¹ √2/2

Write each trigonometric expression as an algebraic expression in u, for u > 0.

tan (arcsec (√1―u²) / u)

Solve each equation for exact solutions.

2 arccos (x/3 - π/3) = 2π