Number 15

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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Number 15

**Evaluating Trigonometric Functions**

**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 \( 30^\circ \), \( 45^\circ \), and \( 60^\circ \):**

**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:**

  23. \(\theta = 30^\circ\), \(\tan\)

  24. \(\theta = 45^\circ\), \(\cos\)

Graphs/Diagrams Explanation:

- **Diagram 13:** A right triangle with angle \( \theta \), hypotenuse 3, and opposite side 1.
  
- **Diagram 14:** A right triangle with angle \( \theta \), adjacent side 1, opposite side 2, and hypotenuse 6.
Transcribed Image Text:**Evaluating Trigonometric Functions** **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 \( 30^\circ \), \( 45^\circ \), and \( 60^\circ \):** **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:** 23. \(\theta = 30^\circ\), \(\tan\) 24. \(\theta = 45^\circ\), \(\cos\) Graphs/Diagrams Explanation: - **Diagram 13:** A right triangle with angle \( \theta \), hypotenuse 3, and opposite side 1. - **Diagram 14:** A right triangle with angle \( \theta \), adjacent side 1, opposite side 2, and hypotenuse 6.
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