**(b) Compute \( \sin 2\theta \). Hint:** \( \sin 2\theta = \sin(\theta + \theta) \) This hint suggests using the angle addition formula for sine. **Problem Statement:**Suppose that \(\sin \theta = \frac{1}{7}\) and \(0 < \theta < \pi/2\).(a) Compute \(\cos \theta\).---**Explanation:**Given that \(\sin \theta = \frac{1}{7}\) and the angle \(\theta\) is in the first quadrant \((0 < \theta < \pi/2)\), we need to find \(\cos \theta\).To find \(\cos \theta\), we use the Pythagorean identity:\[\sin^2 \theta + \cos^2 \theta = 1\]Plug in the value of \(\sin \theta\):\[\left(\frac{1}{7}\right)^2 + \cos^2 \theta = 1\]\[\frac{1}{49} + \cos^2 \theta = 1\]Subtract \(\frac{1}{49}\) from both sides:\[\cos^2 \theta = 1 - \frac{1}{49} = \frac{49}{49} - \frac{1}{49} = \frac{48}{49}\]Take the square root of both sides:\[\cos \theta = \sqrt{\frac{48}{49}} = \frac{\sqrt{48}}{7}\]Since \(\theta\) is in the first quadrant, \(\cos \theta\) is positive. Thus:\[\cos \theta = \frac{\sqrt{48}}{7}\]

Name: **(b) Compute \( \sin 2\theta \). Hint:** \( \sin 2\theta = \sin(\the
Uploaded: 2024-03-20T06:46:55.000Z
Channel: Bartleby
Description: **(b) Compute \( \sin 2\theta \). Hint:** \( \sin 2\theta = \sin(\theta + \theta) \) This hint suggests using the angle addition formula for sine. **Problem Statement:**Suppose that \(\sin \theta = \frac{1}{7}\) and \(0 < \theta < \pi/2\).(a) Compu