3. Unit Circle

Identify what angle, $\(\theta\)$ , satisfies the following conditions.

$\(\tan\]\theta\)=-1$; $\(\cos\]\theta\)$ > $0$

Use reference angles to find the exact value of each expression. Do not use a calculator. cot 19𝜋/6

Find the exact value of each expression. See Example 3. sin 1305°

Use reference angles to find the exact value of each expression. Do not use a calculator. sec 495°

In Exercises 35–60, find the reference angle for each angle. 160°

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

In Exercises 61–86, use reference angles to find the exact value of each expression. Do not use a calculator. tan(-𝜋/4)

In Exercises 35–60, find the reference angle for each angle.

7𝜋/4

Identify the reference angle of each given angle.

$\(\frac{7\pi}{4}\)$ rad

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

Identify what angle, $\(\theta\)$ , satisfies the following conditions.

$\(\sin\]\theta\)=\(\frac\)12$; $\(\tan\]\theta\)$ < $0$

Concept Check Match each angle in Column I with its reference angle in Column II. Choices may be used once, more than once, or not at all. See Example 1. I. II. 5. A. 45° 6. B. 60° 7. -135° C. 82° 8. D. 30° 9. E. 38° 10. F. 32°

In Exercises 35–60, find the reference angle for each angle. -13𝜋/3

Find exact values of the six trigonometric functions of each angle. Rationalize denominators when applicable. See Examples 2, 3, and 5. 405°

Concept Check Match each angle in Column I with its reference angle in Column II. Choices may be used once, more than once, or not at all. See Example 1. I. II. 5. A. 45° 6. B. 60° 7. C. 82° 8. D. 30° 9. E. 38° 10. 480° F. 32°