3. Unit Circle

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

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

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

Write each function in terms of its cofunction. Assume all angles involved are acute angles. See Example 2. sin 45°

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

Determine whether each statement is true or false. If false, tell why. csc 22° ≤ csc 68°

Determine whether each statement is true or false. See Example 4. tan 28° ≤ tan 40°

Determine whether each statement is true or false. See Example 4. cos 28° < sin 28° (Hint: sin 28° = cos 62°)

Determine whether each statement is true or false. See Example 4. cot 30° < tan 40°

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

Give the exact value of each expression. See Example 5. tan 30°

Give the exact value of each expression. See Example 5. sin 30°

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