# Tan on a unit circle

• Jul 2nd 2008, 07:40 PM
Stevo_Evo_22
Tan on a unit circle
Hi again!

I've solved a trig problem and now I have tanx=pi/3, which i know is equal to $\displaystyle \sqrt{3}$.

Im struggling with putting this on a unit circle so I can solve for all of the possible angles. I would appreciate if someone could show me on a unit circle where the possible x's are for this and how i could find out the various angles (of which there are 4).

Thanks,
Steven
• Jul 2nd 2008, 10:19 PM
red_dog
$\displaystyle \displaystyle\tan\frac{\pi}{3}=\sqrt{3}$, not $\displaystyle \tan\sqrt{3}=\frac{\pi}{3}$

Probably the equation is $\displaystyle \tan x=\sqrt{3}$
In this case all solutions are $\displaystyle x=\frac{\pi}{3}+k\pi, \ k\in\mathbf{Z}$
• Jul 3rd 2008, 08:42 AM
Chop Suey
There are two special triangles you can use to find out the trigonometric ratios of the angles: 30, 45, and 60; the 45-45-90 triangle and the 30-60-90 triangle.

Special right triangles - Wikipedia, the free encyclopedia