2. Trigonometric Functions on Right Triangles

Give all six trigonometric function values for each angle θ. Rationalize denominators when applicable. See Examples 5–7. cos θ = 1

Concept CheckSuppose that 90° < θ < 180° .Find the sign of each function value. tan θ/2

Concept CheckSuppose that 90° < θ < 180° .Find the sign of each function value. cot (θ + 180°)

Concept CheckSuppose that ―90° < θ < 90° .Find the sign of each function value. sec θ/2

Concept CheckSuppose that ―90° < θ < 90° .Find the sign of each function value. sec(―θ)

Concept CheckSuppose that ―90° < θ < 90° .Find the sign of each function value. cos(θ―180°)

Concept Check Find a solution for each equation. tan (3θ ― 4°) = 1 / [cot(5θ ― 8°)]

Concept Check Find a solution for each equation. sin(4θ + 2°) csc(3θ + 5°) = 1

Concept Check Find a solution for each equation. sec(2θ + 6°) cos(5θ + 3°) = 1

In Exercises 1–8, use the Pythagorean Theorem to find the length of the missing side of each right triangle. Then find the value of each of the six trigonometric functions of θ.

In Exercises 1–8, use the Pythagorean Theorem to find the length of the missing side of each right triangle. Then find the value of each of the six trigonometric functions of θ.

In Exercises 1–8, use the Pythagorean Theorem to find the length of the missing side of each right triangle. Then find the value of each of the six trigonometric functions of θ.

In Exercises 1–8, use the Pythagorean Theorem to find the length of the missing side of each right triangle. Then find the value of each of the six trigonometric functions of θ.

In Exercises 9–16, use the given triangles to evaluate each expression. If necessary, express the value without a square root in the denominator by rationalizing the denominator.

cos 30°

In Exercises 9–16, use the given triangles to evaluate each expression. If necessary, express the value without a square root in the denominator by rationalizing the denominator.

tan 30°