Evaluating Trigonometric Functions In Exercises 15-22, sketch a right triangle corresponding to the trigonometric function of the acute angle 0. Then find the exact values of the other five trigonometric functions of 0. 15. cos 0 15 17 16. sin 0 %3D 6. 17. sec 0 = 18. tan 0 = %3D %3D 31545

Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.
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## Evaluating Trigonometric Functions

### Exercises 13-14:

**Diagrams:**

- **Figure 13:**
  - A right triangle with sides labeled:
    - Opposite: 3
    - Adjacent: 1
    - Hypotenuse: unmarked
  - Angle labeled as \( \theta \).

- **Figure 14:**
  - A right triangle with sides labeled:
    - Opposite: 2
    - Adjacent: 1
    - Hypotenuse: unmarked (longer side: 3, shorter side: 2)
  - Angle labeled as \( \theta \).

---

**In Exercises 15–22:**

Sketch a right triangle corresponding to the trigonometric function of the acute angle \( \theta \). Then find the exact values of the other five trigonometric functions of \( \theta \).

15. \( \cos \theta = \frac{15}{17} \)

16. \( \sin \theta = \frac{3}{5} \)

17. \( \sec \theta = \frac{6}{5} \)

18. \( \tan \theta = \frac{4}{5} \)

19. \( \sin \theta = \frac{1}{5} \)

20. \( \sec \theta = \frac{17}{7} \)

21. \( \cot \theta = 3 \)

22. \( \csc \theta = 9 \)

---

### Evaluating Trigonometric Functions of 30°, 45°, and 60°

**In Exercises 23–28:** Construct an appropriate triangle to find the missing values. \((0^\circ \leq \theta \leq 90^\circ, 0 \leq \theta \leq \pi/2)\)

| Function | \( \theta \) (deg) | \( \theta \) (rad) | Function Value |
|----------|-------------------|--------------------|----------------|
| 23. tan  | 30°               |                    |                |
| 24. cos  | 45°               |                    |                |

(End of transcription)
Transcribed Image Text:## Evaluating Trigonometric Functions ### Exercises 13-14: **Diagrams:** - **Figure 13:** - A right triangle with sides labeled: - Opposite: 3 - Adjacent: 1 - Hypotenuse: unmarked - Angle labeled as \( \theta \). - **Figure 14:** - A right triangle with sides labeled: - Opposite: 2 - Adjacent: 1 - Hypotenuse: unmarked (longer side: 3, shorter side: 2) - Angle labeled as \( \theta \). --- **In Exercises 15–22:** Sketch a right triangle corresponding to the trigonometric function of the acute angle \( \theta \). Then find the exact values of the other five trigonometric functions of \( \theta \). 15. \( \cos \theta = \frac{15}{17} \) 16. \( \sin \theta = \frac{3}{5} \) 17. \( \sec \theta = \frac{6}{5} \) 18. \( \tan \theta = \frac{4}{5} \) 19. \( \sin \theta = \frac{1}{5} \) 20. \( \sec \theta = \frac{17}{7} \) 21. \( \cot \theta = 3 \) 22. \( \csc \theta = 9 \) --- ### Evaluating Trigonometric Functions of 30°, 45°, and 60° **In Exercises 23–28:** Construct an appropriate triangle to find the missing values. \((0^\circ \leq \theta \leq 90^\circ, 0 \leq \theta \leq \pi/2)\) | Function | \( \theta \) (deg) | \( \theta \) (rad) | Function Value | |----------|-------------------|--------------------|----------------| | 23. tan | 30° | | | | 24. cos | 45° | | | (End of transcription)
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