# How do I find the value of sin 5pi / 6?

Aug 8, 2015

#### Answer:

sin $\frac{5 \pi}{6}$= $\frac{1}{2}$

#### Explanation:

Sin $\frac{5 \pi}{6}$= sin $\left(\pi - \frac{\pi}{6}\right)$= sin $\frac{\pi}{6}$= sin 30 = $\frac{1}{2}$

Another way to think about it is to draw the angle in a Unit circle and create the "new" triangle in Quadrant II.

Drop a perpendicular to the x-axis and you will have the correct triangle to use.

From this triangle, you need the opposite leg length, which is $\frac{1}{2}$.
Since the hypotenuse is equal to 1 in the Unit circle, the opposite leg length is the answer for sine. (dividing by 1 is not necessary)