Find values of... ## Trigonometric Identities and Equations: Half-angle Identities - Problem Type 2**Problem Statement:**Suppose that \( \sin \alpha = -\frac{2}{\sqrt{13}} \) and \( \pi < \alpha < \frac{3\pi}{2} \).Find the exact values of \( \sin \frac{\alpha}{2} \) and \( \tan \frac{\alpha}{2} \).**Solution:**1. **Calculation for \( \sin \frac{\alpha}{2} \):** \[ \sin \frac{\alpha}{2} = \sqrt{\frac{8}{13}} \] This equation represents the value of the sine of half the angle \(\alpha\).2. **Calculation for \( \tan \frac{\alpha}{2} \):** The tan value isn't provided in the text, typically \( \tan \frac{\alpha}{2} \) can be found using the identity: \[ \tan \frac{\alpha}{2} = \frac{1 - \cos \alpha}{\sin \alpha} \quad \text{or another appropriate identity depending on cosine value.} \]Note that these calculations may rely on determining additional trigonometric values not immediately known from \( \sin \alpha \), such as \(\cos \alpha\), typically derived using the Pythagorean identity.**Graph/Diagram Explanation:**There is no graph or diagram depicted in this problem. The text involves algebraic manipulation of trigonometric identities to find half-angle values.

Name: Find values of... ## Trigonometric Identities and Equations: Half-angl
Uploaded: 2024-03-20T06:46:14.000Z
Channel: Bartleby
Description: Find values of... ## Trigonometric Identities and Equations: Half-angle Identities - Problem Type 2**Problem Statement:**Suppose that \( \sin \alpha = -\frac{2}{\sqrt{13}} \) and \( \pi < \alpha < \frac{3\pi}{2} \).Find the exact values of \( \sin \f