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

Oct 16, 2015

See below

#### Explanation:

If you get what a $\frac{\pi}{8}$ degree angle is, then the result will be three times that angle.

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

So, $\frac{\pi}{2}$ will be half of that angle, which is a quarter of a circle.

$\frac{\pi}{4}$ will be half of that angle, and $\frac{\pi}{8}$, again, its half.

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

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

• $\pi$ angle $\to$ west pole;
• $\frac{\pi}{2}$ angle $\to$ north pole;
• $\frac{\pi}{4}$ angle $\to$ north-east;
• $\frac{\pi}{8}$ angle $\to$ east-north-east;

So, $\frac{3 \pi}{8} = \frac{\pi}{4} + \frac{\pi}{8}$ = north-north-east.