7. [4/13 Points] DETAILS PREVIOUS ANSWERS Show that the curve x = 7 cos(t), y = 2 sin(t) cos(t) has two tangents at (0, 0) and find their equations. (Enter your answers as a comma-separated list.) Since x = 7 cos(t) and y = 2 sin(t) cos(t), we have the following. dx -7 sin (t) dt dy dt = 2 cos (t) - 2 sin?(t) At the point (0, 0), we know that cos(t) = 0 , which only occurs at negative |x multiples of -. On the interval [0, 27), this only occurs at the following values. (Enter your answers as a comma-separated list.) At the smallest of these values, dx dy and _ dy So dt dt dx At the largest of these values found to meet the condition in [0, 2n), - dx and dy , SO dy dt dx Thus, there are two tangents to the curve x = 7 cos(t), y = 2 sin(t) cos(t), and their equations are as follows. (Enter your answers as a comma-separated list.) 2x y : X Graph the curve