Using the Unit Circle - Math

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What is $\sin(\pi)$ ?

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If you examine the unit circle, you'll see that that $\sin(\pi)=0$ .

What is $\cos(\pi)$ ?

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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 $(\pi,-1)$ .

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

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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}$)$ ?

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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}$)$ ?

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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}$)$ ?

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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}$)$ ?

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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}$)$ ?

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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}$)$ ?

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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}$)$ ?

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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 $\sin(\pi)$ ?

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If you examine the unit circle, you'll see that that $\sin(\pi)=0$ .

What is $\cos(\pi)$ ?

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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 $(\pi,-1)$ .

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

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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}$)$ ?

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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}$)$ ?

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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}$)$ ?

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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}$)$ ?

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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}$)$ ?

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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}$)$ ?

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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}$)$ ?

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