Show that the curve x = 5 cos(t), y = 7 sin(t) cos(t) has two tangents at (0, 0) and find their equations. (Enter your answers as a comma-separated list.) Since x = 5 cos(t) and y = 7 sin(t) cos(t), we have the following. dx dt dy dt At the point (0, 0), we know that cos(t) = ---Select--- @ , which only occurs at ---Select--- @ 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 and dy , SO dy dt dt dx At the largest of these values found to meet the condition in [0, 27), - dx d dy So dy dt dt dx Thus, there are two tangents to the curve x = 5 cos(t), y = 7 sin(t) cos(t), and their equations are as follows. (Enter your answers as a comma-separated list.) Graph the curve