3. Unit Circle

Determine whether each statement is true or false. If false, tell why. See Example 4.tan² 60° + 1 = sec² 60°

Find all values of θ, if θ is in the interval [0°, 360°) and has the given function value. See Example 6.cos θ = √3 2

Find all values of θ, if θ is in the interval [0°, 360°) and has the given function value. See Example 6.sec θ = -√2

Find all values of θ, if θ is in the interval [0°, 360°) and has the given function value. See Example 6. √3sin θ = - —— 2

Find all values of θ, if θ is in the interval [0°, 360°) and has the given function value. See Example 6. 1cos θ = - — 2

Concept Check Does there exist an angle θ with the function values cos θ = ⅔ and sin θ = ¾?

Suppose θ is in the interval (90°, 180°). Find the sign of each of the following.sec(θ + 180°)

Suppose θ is in the interval (90°, 180°). Find the sign of each of the following.cot(θ + 180°)

Suppose θ is in the interval (90°, 180°). Find the sign of each of the following.sin(-θ)

Concept Check Work each problem.Without using a calculator, determine which of the following numbers is closest to sin 115°: -0.9, -0.1, 0, 0.1, or 0.9.

Concept Check Work each problem.For what angles θ between 0° and 360° is cos θ = sin θ true?

Find exact values of the six trigonometric functions for each angle. Do not use a calculator. Rationalize denominators when applicable.120°

Find all values of θ, if θ is in the interval [0°, 360°) and has the given function value.cos θ = -½

Find all values of θ, if θ is in the interval [0°, 360°) and has the given function value.sec θ = -2√3 3

Evaluate each expression. Give exact values.tan² 120° - 2 cot 240°