If cos a = 0.874 and sin ß = 0.868 with both angles' terminal rays in Quadrant-I, find the tan(a + 3) = Your answers should be accurate to 4 decimal places.
If cos a = 0.874 and sin ß = 0.868 with both angles' terminal rays in Quadrant-I, find the tan(a + 3) = Your answers should be accurate to 4 decimal places.
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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![### Trigonometry Problem
**Problem Statement:**
Given:
\[ \cos \alpha = 0.874 \]
\[ \sin \beta = 0.868 \]
Both angles' terminal rays lie in Quadrant I.
**Task:**
Find the value of:
\[ \tan(\alpha + \beta) = \]
Your answers should be accurate to 4 decimal places.
---
**Hint:**
To solve this problem, use the tangent addition formula:
\[ \tan(\alpha + \beta) = \frac{\tan \alpha + \tan \beta}{1 - \tan \alpha \tan \beta} \]
First, find \( \sin \alpha \) and \( \cos \beta \) using the Pythagorean identity:
\[ \sin^2 \alpha + \cos^2 \alpha = 1 \]
\[ \sin^2 \beta + \cos^2 \beta = 1 \]
Then calculate \( \tan \alpha \) and \( \tan \beta \) using:
\[ \tan \alpha = \frac{\sin \alpha}{\cos \alpha} \]
\[ \tan \beta = \frac{\sin \beta}{\cos \beta} \]
Finally, substitute these values into the tangent addition formula.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1b559ab3-5119-482d-94d5-a98a530a62e8%2Fbee71dd1-492a-48fd-9aad-9300887d7d1e%2F4aqdrx_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Trigonometry Problem
**Problem Statement:**
Given:
\[ \cos \alpha = 0.874 \]
\[ \sin \beta = 0.868 \]
Both angles' terminal rays lie in Quadrant I.
**Task:**
Find the value of:
\[ \tan(\alpha + \beta) = \]
Your answers should be accurate to 4 decimal places.
---
**Hint:**
To solve this problem, use the tangent addition formula:
\[ \tan(\alpha + \beta) = \frac{\tan \alpha + \tan \beta}{1 - \tan \alpha \tan \beta} \]
First, find \( \sin \alpha \) and \( \cos \beta \) using the Pythagorean identity:
\[ \sin^2 \alpha + \cos^2 \alpha = 1 \]
\[ \sin^2 \beta + \cos^2 \beta = 1 \]
Then calculate \( \tan \alpha \) and \( \tan \beta \) using:
\[ \tan \alpha = \frac{\sin \alpha}{\cos \alpha} \]
\[ \tan \beta = \frac{\sin \beta}{\cos \beta} \]
Finally, substitute these values into the tangent addition formula.
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