CPM Homework Help : INT3 Problem 9-66

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9-66.

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

$\sin\left(\frac{\pi}{4}\right)$
Hint: (a)
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.
More Help (a):
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.
Answer (a):
$\frac{\sqrt{2}}{2}$ or $0.707$

$\sin\left(\frac{2\pi}{3}\right)$
Hint (b):
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.
More Help (b):
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.

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