7. Given that when $x$ is in radians, we have
$$
(\sin x)^{\prime}=\cos x \text {. }
$$

then when $x$ is in degrees, the derivative of $\sin x$ is
7. $\frac{\pi}{180} \cos x$.

When $x$ is in degrees,
$$
\begin{array}{l}
\left(\sin x^{\circ}\right)^{\prime}=\left(\sin \frac{\pi x}{180} \text{rad}\right)^{\prime} \\
=\cos \left(\frac{\pi x}{180} \text{rad}\right) \cdot\left(\frac{\pi x}{180} \text{rad}\right)^{\prime} \\
=\frac{\pi}{180} \cos x^{\circ} .
\end{array}
$$