Solve the equation on the interval 0

Question

Solve the equation on the interval 0<(or equal to)theta<2pi
cos(2(theta))=-(sqrt3/2)

anonymous · Answer

$$0\le \theta <2\pi $$

anonymous · Answer

i'm kind of on a time crunch so if anyone can help me do this quickly and in a way i still get it that'd be great.

anonymous · Answer

wait sorry i lied

anonymous · Answer

it's 1/2 not -sqrt3/2

miracrown · Answer

You didn't lie, you made a mistake; that's not lying ;)

anonymous · Answer

true :) aha

anonymous · Answer

but i have to finish like 15 of these problems in 20 minutes so if someone could PLEASE help me quickly that'd be great.. sorry not trying to be be rude in any way.

miracrown · Answer

You wrote the interval, can you write the actual problem we need to solve?

anonymous · Answer

i did .. 
it's $$\sin(2\theta)=1/2$$

anonymous · Answer

or i guess i didn't, please excuse me.

miracrown · Answer

Its alright. Have you attempted it yet?

miracrown · Answer

Are you familiar with the unit circle?

miracrown · Answer

Notice that here the sine value is positive. In which quadrant that has positive sine value? can you tell me?

anonymous · Answer

i know the bare basics

miracrown · Answer

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anonymous · Answer

the second quadrant right?

miracrown · Answer

and the first quadrant

anonymous · Answer

oh yeah cause everything is positive in the first, correct?

miracrown · Answer

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miracrown · Answer

Yes, correct. ...and what angle in the first quadrant that will give us sine equals to 1/2

anonymous · Answer

pi/6?

miracrown · Answer

yes

miracrown · Answer

...and what angle in the second quadrant that will give us sine equals to 1/2

anonymous · Answer

5pi/6

miracrown · Answer

Yep

miracrown · Answer

so, now you know  that is for 2θ

anonymous · Answer

it has a bunch of question marks after the 2... is that supposed to say something?

miracrown · Answer

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