3. Unit Circle

In Exercises 31–38, find a cofunction with the same value as the given expression. sin 7°

In Exercises 31–38, find a cofunction with the same value as the given expression. csc 25°

In Exercises 31–38, find a cofunction with the same value as the given expression. tan 𝜋 9

In Exercises 31–38, find a cofunction with the same value as the given expression. cos 2𝜋 5

In Exercises 41–43, find the exact value of each of the remaining trigonometric functions of θ.

cos θ = 2/5, sin θ < 0

CONCEPT PREVIEW Match each trigonometric function in Column I with its value in Column II. Choices may be used once, more than once, or not at all.

csc 60°

Suppose ABC is a right triangle with sides of lengths a, b, and c and right angle at C. Use the Pythagorean theorem to find the unknown side length. Then find exact values of the six trigonometric functions for angle B. Rationalize denominators when applicable. See Example 1. a = 6, c = 7

Suppose ABC is a right triangle with sides of lengths a, b, and c and right angle at C. Use the Pythagorean theorem to find the unknown side length. Then find exact values of the six trigonometric functions for angle B. Rationalize denominators when applicable. See Example 1. b = 8, c = 11

Suppose ABC is a right triangle with sides of lengths a, b, and c and right angle at C. Use the Pythagorean theorem to find the unknown side length. Then find exact values of the six trigonometric functions for angle B. Rationalize denominators when applicable. See Example 1. a = √2, c = 2

Write each function in terms of its cofunction. Assume all angles involved are acute angles. See Example 2. tan 25.4°

Write each function in terms of its cofunction. Assume all angles involved are acute angles. See Example 2. cos(θ + 20°)

Find one solution for each equation. Assume all angles involved are acute angles. See Example 3. tan α = cot(α + 10°)

Find one solution for each equation. Assume all angles involved are acute angles. See Example 3. sin(2θ + 10°) = cos(3θ - 20°)

Find one solution for each equation. Assume all angles involved are acute angles. See Example 3. cot(5θ + 2°) = tan(2θ + 4°)

Find one solution for each equation. Assume all angles involved are acute angles. See Example 3. sec(3β + 10°) = csc(β + 8°)