solve tan2x - square root of 3 = 0 for principal values of x, and express the solutions in degrees. Please be very specific in the steps you show :) The concept is really new to me, and I want to understand why you do what.

Question

anonymous · Answer

$$\tan 2x=\sqrt{3}=\tan \frac{ \pi }{ 3 },2x=\frac{ \pi }{ 3 },x=?$$

anonymous · Answer

sorry, where does the tan pi/3 come from?

anonymous · Answer

$$\tan 2x=\sqrt{3}=\tan 60,2x=60,x=?$$

anonymous · Answer

$$\tan(whatever)=\sqrt3\
whatever =\frac{\pi}{3}$$

anonymous · Answer

ohhh ok that makes so much more sense now!

anonymous · Answer

so then one of the solutions would be x= 30 degrees?

anonymous · Answer

correct.

anonymous · Answer

no

anonymous · Answer

Oh?

anonymous · Answer

well yes, but it really is $\frac{\pi}{6}$

anonymous · Answer

Ohh ok. Thank you. Are there other solutions too, or is it just that one?

anonymous · Answer

tangent is periodic, there are an infinite number of solutions