Find all points (if any) of horizontal and vertical tangency to the portion of the curve shown. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)x = cos(?) + ? sin(?)y = sin(?) − ? cos(?) −2? ≤ ? ≤ 2? **Problem Statement:**Find all points (if any) of horizontal and vertical tangency to the portion of the curve shown. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)**Parametric Equations:**\[ x = \cos(\theta) + \theta \sin(\theta) \]\[ y = \sin(\theta) - \theta \cos(\theta) \]\[ -2\pi \leq \theta \leq 2\pi \]**Graph Description:**The graph is a plot of the parametric equations described above, displaying a loopy curve within the Cartesian plane. It extends horizontally between approximately -8 and 6 on the x-axis and vertically between -8 and 8 on the y-axis. The curve has various loops, indicating complex behavior over the range of \(\theta\). The axes are labeled, with x and y marked at intervals of 2. The curve appears symmetrical along some parts and may have multiple points of tangency which need to be calculated.

The equation of the given curve is to find all the points or values where the tangents are either vertical or horizontal.The slope of the tangent of a curve is represented by , if the tangent is horizontal then its slope is zero,if the tangent is vertical then the slope is undefined or .It is known that for ,and for undefined.Evaluate by differentiating with respect to .Evaluate the slope of the tangents, .When the tangent are horizontal then the slope is zero.When the tangent is vertical then slope is undefined.The horizontal tangents occur for the following values of , .The vertical tangents occur for the following values of , .