What are the values of theta in the interval 0

Question

What are the values of theta in the interval 0<theta<360 that satisfy the equation (theta x)-(radical 3)=0 ?
1) 60º, 240º    (see note below)
2) 72º, 252º  
3) 72º, 108º, 252º, 288º        
4) 60º, 120º, 240º, 300

anonymous · Answer

$$0\le \theta \le 360$$
$$\tan \theta -\sqrt{3} =0$$

tkhunny · Answer

You can't find even one?

You might want to give a 30-60-90 right triangle a really close look.

anonymous · Answer

Well, I know there's 60, but that's it. Should I just know the value of 60º, 120º, 240º, and 300 by heart, or is there another way?

tkhunny · Answer

Good, but you should have mentioned that you already had one solution.

60º is in Quadrant I.  Can you think of another quadrant where the tangent has the same sign?  II?  III?, IV?

anonymous · Answer

III

anonymous · Answer

180<270, so 240.

tkhunny · Answer

Reference Angle 60º
Quadrant I and III

Done.  Good work.