Question

How to put the radian angle 3pi/8 point on a unit circle?

Answer 1

See below

Explanation:

If you get what a `pi/8` degree angle is, then the result will be three times that angle.

Let's go for recursive divisions. We know that `\pi` is a straight angle, `180°`, half a circle.

So, `pi/2` will be half of that angle, which is a quarter of a circle.

`pi/4` will be half of that angle, and `pi/8`, again, its half.

We can also write `{3pi}/8` as `pi/4+pi/8`. So, starting from half a quarter of a circle, we must take another step of `pi/8`.

I'll try to identify this whole procedure with cardinal points:

• `pi` angle `->` west pole;
• `pi/2` angle `->` north pole;
• `pi/4` angle `->` north-east;
• `pi/8` angle `->` east-north-east;

So, `{3pi}/8=pi/4+pi/8` = north-north-east.