5. Inverse Trigonometric Functions and Basic Trigonometric Equations

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]

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

y = tan⁻¹ (―√3)

Graph each inverse circular function by hand.

y = arcsec [(1/2)x]

Evaluate each expression without using a calculator.

tan (arccos 3/4)

Evaluate each expression without using a calculator.

cos (tan⁻¹ (-2))

Evaluate each expression without using a calculator.

sin (2 tan⁻¹ (12/5))

Evaluate each expression without using a calculator.

cos (2 arctan (4/3))

Evaluate each expression without using a calculator.

sin (2 cos⁻¹ (1/5))

Evaluate each expression without using a calculator.

sec (sec⁻¹ 2)

Evaluate each expression without using a calculator.

cos (tan⁻¹ (5/12) - tan⁻¹ (3/4))