Math - Using the Unit Circle

What is $\sin(\frac{\pi}{2})$ ?

$\frac{\sqrt2}{2}$

$2\pi$

Explanation

If you examine the unit circle, you'll see that the the $\sin(\frac{\pi}{2})=1$ . If you were to graph a sine function, you would also see that it crosses through the point $(\frac{\pi}{2},1)$ .

What is $\cos(\frac{\pi}{2})$ ?

$\frac{\sqrt2}{}2$

$\frac{1}{3}$

Explanation

Using the unit circle, you can see that $\cos(\frac{\pi}{2})=0$ . If you were to graph a cosine function, you would also see that it crosses through the point $(\frac{\pi}{2},0)$ .

What is $\cos(\frac{2\pi}{3})$ ?

$-\frac{1}{2}$

$\frac{1}{2}$

Explanation

If you look at the unit circle, you'll see that $\cos(\frac{2\pi}{3})=\frac{1}{2}$ . You can also think of this as the cosine of $60^\circ$ , which is also $\frac{1}{2}$ .

What is $\sin(\frac{2\pi}{3})$ ?

$\frac{\sqrt3}{2}$

$-\frac{\sqrt3}{2}$

$\frac{1}{2}$

Explanation

If you look at the unit circle, you'll see that $\sin(\frac{2\pi}{3})=\frac{\sqrt3}{2}$ . You can also think of this as the sine of $60^\circ$ , which is also $\frac{\sqrt3}{2}$ .

What is $\sin(\frac{3\pi}{4})$ ?

$\frac{\sqrt{2}}{2}$

$\frac{1}{2}$

$\frac{-\sqrt2}{2}$

Explanation

Using the unit circle, $\sin(\frac{3\pi}{4})=\frac{\sqrt2}{2 }$ . You can also think of this as the sine of $135^\circ$ , which would also be $\frac{\sqrt2}{2}$ .

What is $\cos (\frac{3\pi}{4})$ ?

$-\frac{\sqrt2}{2}$

$\frac{\sqrt2}{2}$

$\frac{2\sqrt2}{2}$

Explanation

Using the unit circle, you can see that the $\cos (\frac{3\pi}{4})=-\frac{\sqrt2}{2}$ . Since the angle is in Qudrant II, sine is positive and cosine is negative.

What is $\sin(\frac{\pi}{4})$ ?

$\frac{\sqrt2}{2}$

$-\frac{\sqrt2}{2}$

$\frac{1}{2}$

Explanation

Using the unit circle, $\sin(\frac{\pi}{4})=\frac{\sqrt2}{2 }$ . You can also think of this as the sine of $45^\circ$ , which would also be $\frac{\sqrt2}{2}$ .

What is $\cos(\frac{\pi}{4})$ ?

$\frac{\sqrt2}{2}$

$\frac{1}{2}$

$\frac{2\sqrt2}{2}$

Explanation

Using the unit circle, $\cos(\frac{\pi}{4})=\frac{\sqrt2}{2 }$ . You can also think of this as the cosine of $45^\circ$ , which would also be $\frac{\sqrt2}{2}$ .

What is $\cos(\pi)$ ?

$\frac{\sqrt2}{2}$

$\frac{\sqrt3}{2}$

Explanation

If you examine the unit circle, you'll see that the value of $\cos(\pi)=-1$ . You can also get this by examining a cosine graph and you'll see it crosses the point $(\pi,-1)$ .