(Solved): Find the points at which the following polar curve has a horizontal or a vertical tangent line. \[ ...

Find the points at which the following polar curve has a horizontal or a vertical tangent line. \[ r=1+\sin \theta \] Find \( \frac{\mathrm{dy}}{\mathrm{dx}} \) as a function of \( \theta \) \[ \frac{d y}{d x}=\frac{2 \sin 2 \theta+\cos \theta}{2 \cos 2 \theta-\sin \theta} \] Identify the points where the curve has a horizontal tangent line. Select all that apply. A. \( \left(2, \frac{\pi}{2}\right) \) B. \( \left(\frac{3}{2}, \frac{7 \pi}{6}\right) \) \( \square E \cdot\left(2, \frac{3 \pi}{2}\right) \) D. \( \left(\frac{1}{2}, \frac{7 \pi}{6}\right) \) H. \( \left(0, \frac{3 \pi}{2}\right) \) G. \( \left(\frac{3}{2}, \frac{5 \pi}{6}\right) \) Identify the points where the curve has a vertical tangent line. Select all that apply. A. \( \left(\frac{3}{2}, \frac{5 \pi}{6}\right) \) B. \( \left(\frac{1}{2}, \frac{7 \pi}{6}\right) \) D. \( \left(\frac{3}{2}, \frac{11 \pi}{6}\right) \) E. \( \left(2, \frac{3 \pi}{2}\right) \) G. \( \left(\frac{3}{2}, \frac{\pi}{6}\right) \)