3. Unit Circle

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. I II1. A. √32. B. 13. C. ½4. D. √35. csc 60° 26. E. 2√3 3 F. √3 3 G. 2 H. √2 2 I. √2

Find one solution for each equation. Assume all angles involved are acute angles.cos(3θ + 11°) = sin( 7θ + 40°) 5 10

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.

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°

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

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

In Exercises 17–20, θ is an acute angle and sin θ and cos θ are given. Use identities to find tan θ, csc θ, sec θ, and cot θ. Where necessary, rationalize denominators.__sin θ = 6, cos θ = √137 7

In Exercises 21–24, θ is an acute angle and sin θ is given. Use the Pythagorean identity sin²θ + cos²θ = 1 to find cos θ.sin θ = 6/7

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

In Exercises 21–24, θ is an acute angle and sin θ is given. Use the Pythagorean identity sin²θ + cos²θ = 1 to find cos θ.__sin θ = √398