*Trigonometric Functions*
Consider the equation 3tan2(x)−1=0.
The solutions of this equation over the interval [0, π] are?
*Please help will give medal*

Question

anonymous · Answer

solve $$\tan(x)=\pm\frac{1}{\sqrt{3}}$$

princessaurora · Answer

x=π6±πn,7π6±πn

princessaurora · Answer

Is that correct?

anonymous · Answer

yeah i guess 
$\frac{\pi}{6}$ works for sure

anonymous · Answer

yeah that looks good except it said only on the interval $$[0,\pi]$$

princessaurora · Answer

what about the second one?

anonymous · Answer

you have a general solution there 
you only want the solution on $[0,\pi]$ not a general one

princessaurora · Answer

ok so can you help me with getting that?

anonymous · Answer

sure

anonymous · Answer

$$\frac{\pi}{6}$$ works because $$\tan(\frac{\pi}{6})=\frac{1}{\sqrt3}$$
do you know why (just asking)

princessaurora · Answer

because you subtracted it?

anonymous · Answer

the other one on that interval is $\frac{5\pi}{6}$

princessaurora · Answer

Okay thanks so much! I appreciate it I got it now.

anonymous · Answer

yw