Find the exact values for the six trigonometric functions of the angle 0 in the figure. 5/26 17
Find the exact values for the six trigonometric functions of the angle 0 in the figure. 5/26 17
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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Question
![**Trigonometric Functions of Right Triangle**
**Problem Statement:**
Find the exact values for the six trigonometric functions of the angle \( \theta \) in the figure.
**Figure Description:**
The figure shows a right triangle with one angle labeled \( \theta \). The sides of the triangle are as follows:
- The side opposite angle \( \theta \) has a length of 17.
- The side adjacent to angle \( \theta \) has a length of 19.
- The hypotenuse (the side opposite the right angle) has a length of \( 5\sqrt{26} \).
**Understanding the Trigonometric Functions:**
1. **Sine (\(\sin \theta\))**: The ratio of the length of the side opposite \( \theta \) to the length of the hypotenuse.
\[
\sin \theta = \frac{17}{5\sqrt{26}}
\]
2. **Cosine (\(\cos \theta\))**: The ratio of the length of the side adjacent to \( \theta \) to the length of the hypotenuse.
\[
\cos \theta = \frac{19}{5\sqrt{26}}
\]
3. **Tangent (\(\tan \theta\))**: The ratio of the length of the side opposite \( \theta \) to the length of the side adjacent to \( \theta \).
\[
\tan \theta = \frac{17}{19}
\]
4. **Cosecant (\(\csc \theta\))**: The reciprocal of sine.
\[
\csc \theta = \frac{5\sqrt{26}}{17}
\]
5. **Secant (\(\sec \theta\))**: The reciprocal of cosine.
\[
\sec \theta = \frac{5\sqrt{26}}{19}
\]
6. **Cotangent (\(\cot \theta\))**: The reciprocal of tangent.
\[
\cot \theta = \frac{19}{17}
\]
These ratios help in determining the trigonometric functions values for angle \( \theta \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Feb5c4afe-031f-4485-8b26-650e5f71f638%2F23e688b9-23ab-4a92-8112-e72705ac5b6f%2Fypncb2k_processed.png&w=3840&q=75)
Transcribed Image Text:**Trigonometric Functions of Right Triangle**
**Problem Statement:**
Find the exact values for the six trigonometric functions of the angle \( \theta \) in the figure.
**Figure Description:**
The figure shows a right triangle with one angle labeled \( \theta \). The sides of the triangle are as follows:
- The side opposite angle \( \theta \) has a length of 17.
- The side adjacent to angle \( \theta \) has a length of 19.
- The hypotenuse (the side opposite the right angle) has a length of \( 5\sqrt{26} \).
**Understanding the Trigonometric Functions:**
1. **Sine (\(\sin \theta\))**: The ratio of the length of the side opposite \( \theta \) to the length of the hypotenuse.
\[
\sin \theta = \frac{17}{5\sqrt{26}}
\]
2. **Cosine (\(\cos \theta\))**: The ratio of the length of the side adjacent to \( \theta \) to the length of the hypotenuse.
\[
\cos \theta = \frac{19}{5\sqrt{26}}
\]
3. **Tangent (\(\tan \theta\))**: The ratio of the length of the side opposite \( \theta \) to the length of the side adjacent to \( \theta \).
\[
\tan \theta = \frac{17}{19}
\]
4. **Cosecant (\(\csc \theta\))**: The reciprocal of sine.
\[
\csc \theta = \frac{5\sqrt{26}}{17}
\]
5. **Secant (\(\sec \theta\))**: The reciprocal of cosine.
\[
\sec \theta = \frac{5\sqrt{26}}{19}
\]
6. **Cotangent (\(\cot \theta\))**: The reciprocal of tangent.
\[
\cot \theta = \frac{19}{17}
\]
These ratios help in determining the trigonometric functions values for angle \( \theta \).
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