5. Inverse Trigonometric Functions and Basic Trigonometric Equations

Evaluate the expression using a calculator. Express your answer in radians, rounding to two decimal places.

$\tan^{-1}\left(5\right)$

Evaluate the expression using a calculator. Express your answer in radians, rounding to two decimal places.

$\sin^{-1}\left(-\frac13\right)$

Evaluate the expression using a calculator. Express your answer in radians, rounding to two decimal places.

$\cos^{-1}\left(\frac14\right)$

Decide whether each statement is true or false. If false, explain why.

The tangent and secant functions are undefined for the same values.

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)