3. Unit Circle

Find each exact function value. See Example 2.

tan 3π/4

Determine whether each statement is true or false. See Example 4. csc 20° < csc 30°

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

cos θ = 2/5, sin θ < 0

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

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

Find exact values or expressions for sin A, cos A, and tan A. See Example 1.

Determine whether each statement is true or false. If false, tell why. tan 60° ≥ cot 40°

Find the exact value of s in the given interval that has the given circular function value.

[ 0, π/2] ; cos s = √2/2

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 = 5, b = 12

The formula ω = θ/t can be rewritten as θ = ωt. Substituting ωt for θ converts s = rθ to s = rωt. Use the formula s = rωt to find the value of the missing variable.

r = 6 cm, ω = π/3 radians per sec, t = 9 sec

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°

Find the angular speed ω for each of the following.

a gear revolving 300 times per min