Understanding Math formula that excludes a part of the circle

Question

I just came across the below line of code , in javascript:

        additionalAngelPI = (90 / 180) * Math.PI;

This is a Math question though , basically the above formula will exclude 90 degrees of the circle , but how really does this formula work , why is 90 decided by 180 ? and then multiplied by PI ?

I am not a genious at math but i do understand the basics of circular maths I.E. PI is the ratio between the diameter and the circumference etc.

If anybody can help me understand the above formula it would be great.

Answer 1

Observe that in order to convert $90^{\text{o}}$ to radian units, we do as follows:

$$90^{\text{o}} = 90 \cdot \frac{\pi}{180} \,\text{rad} = \frac{90\pi}{180} \,\text{rad} = \frac{\pi}{2} \,\text{rad}$$

since $$\pi \,\text{rad} = 180^{\text{o}}.$$

Answer 2

In computers and mathematics trigonometric functions are dealt with using radians because the formulas to calculate them using series and much else is friendlier then.

There are $2\pi$ radians in a circle, which gives us that $180^\circ = \pi$ or equivalently $$1^\circ = \frac{\pi}{180}$$ and the times 90 is fairly evident then.