### Home > A2C > Chapter 8 > Lesson 8.1.5 > Problem8-79

8-79.

Calculate each of the following values. Express your answers both exactly and as decimal approximations.

1. $\sin\left(\frac{\pi}{4}\right)$

Draw a unit circle and locate $\frac{\pi}{4}$ radians.

Remember that a full circle as $2\pi$ radians and a half circle has $\pi$ radians.

How many degrees is equivalent to $\frac{\pi}{4}$ radians?

Draw a right triangle and use the special triangle relationship to find the exact value.

$\frac{\sqrt{2}}{2}$ or $0.707$

1. $\sin\left(\frac{2\pi}{3}\right)$

Since $\pi$ is equivalent to $180^\circ$$\frac{1}{3}$ of $\pi$ is $60^\circ$.
What is $\frac{2}{3}$ of $\pi$? Locate $\frac{2\pi}{3}$  on the unit circle.

Draw a right triangle.
Notice that $60^\circ$ is your reference angle.
Use the $30^\circ-60^\circ-90^\circ$ relationship to find the exact value.