The slope at the point $(\pi, 7)$ is 0.
Work Step by Step
To find $y'$, we find the derivatives of the smaller functions and we add them together. The derivative of $-2cos(t)$ is $(-2)(-1)(sin(t))$ which is $2sin(t)$. The derivative of $5$ is $0$. Adding everything together gives us $y' = 2sin(t)$. To find the slope, we evaluate the derivative at $t = \pi$ which gives us $y' = 2sin(\pi) = 0$. Hence the slope at the point $(\pi, 7)$ is $0$.