should I insert angle in radians or degrees for sun radiance model (sinusoidal)?

Question

If I have the following model function for sun radiance through a day,

$$ P(h) = 0.3 \pi \sin(\frac{h\cdot\pi}{12}-\frac{7\pi}{12}) [\frac{kWh}{m^2}] $$

Where $h$ is the hour of the day and the variable I don't know how to treat it. The solutions fits if I set my calculator in radians instead of degrees but I can't comprehend why.

Thanks in advance.

Answer 1

Note that the sine function argument increases by $2\pi$ when $h$ increases by $24$ hours, so that is one cycle. This means you should use radians.

Answer 2

The $\sin$ function, in its general implementation, will almost always take radians as an input. I would say that unless you're explicitly told the angle measure is in degrees, use radians. Even if you're given degrees I would suggest converting to radians (multiply by $\pi/180$),

$$ x \text{ rad} = \frac{x^\circ \cdot \pi}{180} $$

In your example, the $\pi$ inside the $\sin$ function is a hint that you're using radians, because $\pi$ is an angle measure in radians ($ \pi \text{ rad} = 180 \text{ deg}$).