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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°.
Related questions
Question
Solve #9
![### Trigonometry Problems and Solutions
#### Problem 9
**Task:**
Write an expression involving only cosine and/or sine for the equation:
\[
\tan \theta + \csc \theta
\]
**Solution Steps:**
1. **Definition of Cosecant:**
\[
\csc \theta = \frac{1}{\sin \theta}
\]
2. **Expression Conversion:**
Using the relationship for sine, the expression can be rewritten as:
\[
= \sin \theta \cdot (0.275)
\]
Evaluating:
\[
= 0.276 \, \text{radians}
\]
#### Problem 10
**Task:**
A straight-line bike path section is 400 feet long and loses 18 feet in elevation from start to finish. What is its angle of depression (in degrees rounded correctly to two decimal places)?
**Solution:**
1. **Concept:**
The angle of depression can be found using the tangent ratio. In this scenario, the tangent of the angle will be the ratio of the change in elevation to the length of the path.
2. **Formula:**
\[
\tan(\text{angle of depression}) = \frac{\text{change in elevation}}{\text{length of path}} = \frac{18}{400}
\]
3. **Calculations:**
- Calculate the angle using an inverse tangent function to determine the angle of depression in degrees.
This transcribed content is suitable for educational use, presenting two trigonometry problems alongside their explanations and solutions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2816e768-d46c-42f8-b287-986238abcd2a%2Fa0f82985-da54-40c1-8f36-c692c011d57f%2Fk5b6s8s_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Trigonometry Problems and Solutions
#### Problem 9
**Task:**
Write an expression involving only cosine and/or sine for the equation:
\[
\tan \theta + \csc \theta
\]
**Solution Steps:**
1. **Definition of Cosecant:**
\[
\csc \theta = \frac{1}{\sin \theta}
\]
2. **Expression Conversion:**
Using the relationship for sine, the expression can be rewritten as:
\[
= \sin \theta \cdot (0.275)
\]
Evaluating:
\[
= 0.276 \, \text{radians}
\]
#### Problem 10
**Task:**
A straight-line bike path section is 400 feet long and loses 18 feet in elevation from start to finish. What is its angle of depression (in degrees rounded correctly to two decimal places)?
**Solution:**
1. **Concept:**
The angle of depression can be found using the tangent ratio. In this scenario, the tangent of the angle will be the ratio of the change in elevation to the length of the path.
2. **Formula:**
\[
\tan(\text{angle of depression}) = \frac{\text{change in elevation}}{\text{length of path}} = \frac{18}{400}
\]
3. **Calculations:**
- Calculate the angle using an inverse tangent function to determine the angle of depression in degrees.
This transcribed content is suitable for educational use, presenting two trigonometry problems alongside their explanations and solutions.
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