Use the appropriate reciprocal identity to find the exact value of csc 0 for the given value of sin 8. 3 sin 8= csc 8= (Type an integer or a fraction. )
Use the appropriate reciprocal identity to find the exact value of csc 0 for the given value of sin 8. 3 sin 8= csc 8= (Type an integer or a fraction. )
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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![**Using Reciprocal Identities in Trigonometry**
To determine the exact value of \( \csc \theta \) from the given \( \sin \theta \):
Given:
\[ \sin \theta = -\frac{3}{5} \]
To find \( \csc \theta \), use the reciprocal identity of sine:
\[ \csc \theta = \frac{1}{\sin \theta} \]
Applying the given value of \( \sin \theta \):
\[ \csc \theta = \frac{1}{-\frac{3}{5}} \]
Simplify the expression by multiplying the numerator and denominator by -1:
\[ \csc \theta = -\frac{1}{\frac{3}{5}} = -\frac{5}{3} \]
So, the exact value of \( \csc \theta \) is:
\[ \csc \theta = -\frac{5}{3} \]
**Answer Format:**
(Type an integer or a fraction.)
\[ \boxed{-\frac{5}{3}} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9b70f989-f4fe-4180-9465-a46932af6785%2F25fc6ff0-e31a-4df6-bb16-abaa485ef143%2F6i52bd_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Using Reciprocal Identities in Trigonometry**
To determine the exact value of \( \csc \theta \) from the given \( \sin \theta \):
Given:
\[ \sin \theta = -\frac{3}{5} \]
To find \( \csc \theta \), use the reciprocal identity of sine:
\[ \csc \theta = \frac{1}{\sin \theta} \]
Applying the given value of \( \sin \theta \):
\[ \csc \theta = \frac{1}{-\frac{3}{5}} \]
Simplify the expression by multiplying the numerator and denominator by -1:
\[ \csc \theta = -\frac{1}{\frac{3}{5}} = -\frac{5}{3} \]
So, the exact value of \( \csc \theta \) is:
\[ \csc \theta = -\frac{5}{3} \]
**Answer Format:**
(Type an integer or a fraction.)
\[ \boxed{-\frac{5}{3}} \]
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