5. Inverse Trigonometric Functions and Basic Trigonometric Equations

Which one of the following equations has solution 0?

a. arctan 1 = x

b. arccos 0 = x

c. arcsin 0 = x

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

tan (sin⁻¹ u/(√u² + 2))

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

sec (arccot (√4―u² )/ u)

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

y = 6 cos x/4 , for x in [0, 4π]

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

y = sec⁻¹ (―2)

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

y = ― 2 cos 5x , for x in [0, π/5]

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

y = sin⁻¹ 0

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

y = arccot (―1)

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

y = sin⁻¹ (―1)

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

y = sin x ―2 , for x in [―π/2. π/2]

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

y = cos⁻¹ (―1)

Give the degree measure of θ. Do not use a calculator.

θ = arcsin (―√3/2)

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

y = ―4 + 2 sin x , for x in [―π/2. π/2]

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

y = tan⁻¹ 1