3. Unit Circle

Without using a calculator, determine which of the two values is greater.

tan 1 or tan 2

Find the exact values of (a) sin s, (b) cos s, and (c) tan s for each real number s. See Example 1.

s = 2π

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

Find each exact function value.

tan π/3

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

Find the exact values of (a) sin s, (b) cos s, and (c) tan s for each real number s. See Example 1.

s = π/2

In Exercises 1–4, a point P(x, y) is shown on the unit circle corresponding to a real number t. Find the values of the trigonometric functions at t.

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