What is the integration of Integration of sin(x°) dx.

Question

Integration of $\int \sin(x^{\circ}) \operatorname{d}x$. The '$x$' is ok but this confuses me by creating '$x^{\circ}$'.This is not the differential like to solve it by chain rule. I thought the answer could be '$-\cos x/x^{\circ}$' but not sure.

Answer 1

Let consider a change of variable

$$y=x\cdot \frac{\pi}{180} \implies dy=\frac{\pi}{180}dx$$

therefore

$$\int \sin x° \,dx=\frac{180}{\pi}\int \sin \left(\frac{180}{\pi}y\right) \,\,dy=-\cos\left(\frac{180}{\pi}y\right) +c=-\cos x° +c $$

Answer 2

When talking about angles, $x^\circ$ is the same as $x\cdot\frac{\pi}{180}$. In fact, in at least one online graphing calculator that I know of, the symbol $^\circ$ isn't a function or anything, it is actually encoded as the constant $\frac{\pi}{180}$.

Answer 3

$\displaystyle\int \sin(x°) \,dx=\int \sin(\frac{x\pi}{180}) \,dx=-\dfrac{\cos(\dfrac{x\pi}{180})}{\dfrac{\pi}{180}}+c$