Question

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?

Answer 1

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

Answer 2

Use unit circle.

Answer 3

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

Answer 4

np :)