4. Suppose that cos(A) = m , and A is in quadrant I. Then determine sin in terms of m. sin

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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**Problem 4:** Suppose that \( \cos(A) = m \), and \( A \) is in quadrant I. Then determine \( \sin\left(\frac{A}{2}\right) \) in terms of \( m \).

\[ \sin\left(\frac{A}{2}\right) = \underline{\hspace{3cm}} \]

---

**Explanation**

This problem is asking to find the sine of half an angle, \( \sin\left(\frac{A}{2}\right) \), given that the cosine of the angle \( A \) is \( m \), and \( A \) is in the first quadrant. 

To solve this, we may use the half-angle identity for sine:

\[
\sin\left(\frac{A}{2}\right) = \sqrt{\frac{1 - \cos(A)}{2}}
\]

Given \( \cos(A) = m \), substitute \( m \) for \( \cos(A) \):

\[
\sin\left(\frac{A}{2}\right) = \sqrt{\frac{1 - m}{2}}
\]
Transcribed Image Text:**Problem 4:** Suppose that \( \cos(A) = m \), and \( A \) is in quadrant I. Then determine \( \sin\left(\frac{A}{2}\right) \) in terms of \( m \). \[ \sin\left(\frac{A}{2}\right) = \underline{\hspace{3cm}} \] --- **Explanation** This problem is asking to find the sine of half an angle, \( \sin\left(\frac{A}{2}\right) \), given that the cosine of the angle \( A \) is \( m \), and \( A \) is in the first quadrant. To solve this, we may use the half-angle identity for sine: \[ \sin\left(\frac{A}{2}\right) = \sqrt{\frac{1 - \cos(A)}{2}} \] Given \( \cos(A) = m \), substitute \( m \) for \( \cos(A) \): \[ \sin\left(\frac{A}{2}\right) = \sqrt{\frac{1 - m}{2}} \]
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