## anonymous 3 years ago Evaluate exactly in radians: arctan(1/sqrt(3)). I know it equals tan(x)=sqrt(3)/3 and the answer is pi/6 but I do not know why. Can someone explain?

1. myininaya

$\arctan(\frac{1}{\sqrt{3}})=\arctan(\frac{\frac{1}{2}}{\frac{\sqrt{3}}{2}})$ The range of arctan( ) is -pi/2 to pi/2 For when do you have from -pi/2 to pi/2 that $\tan( )=\frac{\sin( )}{\cos( )}=\frac{\frac{1}{2}}{\frac{\sqrt{3}}{2}}$

2. myininaya

Use unit circle.

3. anonymous

Ah, your explanation is exactly what I needed to see. I never though about the fact that the sine and cosine would have common denominators and therefore cancel. Thank you

4. myininaya

np :)

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