# sin of what is equal to sqrt3/2?

May 3, 2018

$\sin 60$ degrees or $\frac{\pi}{3}$ radians

#### Explanation:

In a 30-60-90 triangle, the sides are in the ratio $x : x \sqrt{3} : 2 x$ (smallest leg:longest leg:hypotenuse).

$\sin$ is opposite side over hypotenuse

The opposite side for the $90$ degree angle is the hypotenuse, so $\sin 90$ is $1$

The opposite side for the $30$ degree angle is the smallest leg ($x$).

The opposite side for the $60$ degree angle is the longest leg ($x \sqrt{3}$). $\frac{x \sqrt{3}}{2 x} = \frac{\sqrt{3}}{2}$

May 3, 2018

$\rightarrow x = n \pi + {\left(- 1\right)}^{n} \cdot \left(\frac{\pi}{3}\right)$ where $n \rightarrow Z$

#### Explanation:

Let $\sin x = \frac{\sqrt{3}}{2}$

$\rightarrow \sin x = \sin \left(\frac{\pi}{3}\right)$

$\rightarrow x = n \pi + {\left(- 1\right)}^{n} \cdot \left(\frac{\pi}{3}\right)$ where $n \rightarrow Z$