The slope at the point $(0, 0)$ is $3$.
Work Step by Step
To find the derivative of $y$, we find the derivative of the smaller functions and we add them together. The derivative of $4sin(\theta)$ is $4cos(\theta)$ ( you should remember that $(sin(x)'=cos(x))$ and that $(cos(x)'=-sin(x))$). The derivative of $-\theta$ is $-1$. Adding everything together gives $y' = 4cos(\theta)-1$. To find the slope, substitute the x-coordinate into the derivative. Plugging in $\theta = 0$ gives us $y' = 4cos(0)-1 = 4-1 = 3$ hence the slope at the point $(0, 0)$ is $3$.