5. Inverse Trigonometric Functions and Basic Trigonometric Equations

Solve each equation for exact solutions over the interval [0, 2π).

tan² x + 3 = 0

Evaluate the expression.

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

Evaluate the expression.

$\(\sin\)^{-1}\(\left\)(\(\cos\[\frac{2\pi}{3}\]\right\))$

Evaluate the expression.

$\(\cos\]\left\)(\(\cos\)^{-1}\(\left\)(-\(\sqrt\)3\(\right\))\(\right\))$

Evaluate the expression.

$\(\cos\)^{-1}\(\left\)(\(\cos\[\left\)(\(\frac{\pi}{2}\]\right\))\(\right\))$

Evaluate the expression.

$\(\tan\)^{-1}\(\left\)(\(\tan\[\frac{2\pi}{3}\]\right\))$

Evaluate the expression.

$\(\tan\[\left\)(\(\cos\)^{-1}\(\frac{12}{13}\]\right\))$

Evaluate the expression.

$\(\sin\[\left\)(\(\tan\)^{-1}\(\frac{15}{8}\]\right\))$

Evaluate the expression.

$\(\cos\[\left\)(\(\sin\)^{-1}\(\left\)(-\(\frac{7}{25}\]\right\))\(\right\))$

In Exercises 39–54, find the exact value of each expression, if possible. Do not use a calculator. sin(sin⁻¹ 0.9)

In Exercises 39–54, find the exact value of each expression, if possible. Do not use a calculator. tan (tan⁻¹ 125)

In Exercises 83–94, use a right triangle to write each expression as an algebraic expression. Assume that x is positive and that the given inverse trigonometric function is defined for the expression in x. tan (cos⁻¹ x)

In Exercises 83–94, use a right triangle to write each expression as an algebraic expression. Assume that x is positive and that the given inverse trigonometric function is defined for the expression in x. cos (sin⁻¹ 1/x)

In Exercises 83–94, use a right triangle to write each expression as an algebraic expression. Assume that x is positive and that the given inverse trigonometric function is defined for the expression in x. sec (cos⁻¹ 1/x)

In Exercises 63–82, use a sketch to find the exact value of each expression. tan (cos⁻¹ 5/13)