# How do you find the exact values sin (pi/6) using the special triangles?

Aug 19, 2015

$\sin \left(\frac{\pi}{6}\right) = \frac{1}{2}$
$\textcolor{w h i t e}{\text{XXXXXXXX}}$(see below for use of special triangle)

#### Explanation:

An equilateral triangle has angles of $\frac{\pi}{3}$;
splitting an equilateral triangle as in the image below gives a $\frac{\pi}{6}$ angle

(The $\sqrt{3}$ length is derived using the Pythagorean Theorem).

By definition: $\sin = \text{opposite"/"hypotenuse}$

In this case $\sin \left(\frac{\pi}{6}\right) = \frac{1}{2}$