Help me find three solutions for theta!! Has to be between 360 degrees and -360 degrees

1.) sin (theta) = sin (15)
2.) sin (theta) = -sin (60)
3.) sin (theta) = 0.5
4.) sin (theta) = -0.71

Question

Help me find three solutions for theta!! Has to be between 360 degrees and -360 degrees

1.) sin (theta) = sin (15) 
2.) sin (theta) = -sin (60)
3.) sin (theta) = 0.5
4.) sin (theta) = -0.71

anonymous · Answer

Let me try and understand this better so for the first one you have $$\sin \theta= \sin 15$$ and you're just trying to find theta? Nothing else, right?

anonymous · Answer

Correct.

anonymous · Answer

well if you multiply sin by sin inverse (which looks like this) $$\sin^{-1}  $$

anonymous · Answer

you can cancel out sin

anonymous · Answer

so if you multiple sin inverse on both sides you get $$\theta=15$$

anonymous · Answer

Does that make sense?

anonymous · Answer

Yeah... So I liked at the unit circle and it seems that theta is basically similar around the whole thing

anonymous · Answer

OK I see you want THREE solutions for theta that makes more sense ok hold on

anonymous · Answer

Well clearly the first one is 15 degrees, which can also be stated as pi/12 radians, and since sin is the y value and at 30 degrees it is 1/2 and 15 degrees is half of that, it can also be stated as 1/4

anonymous · Answer

Is that what you are looking for?

anonymous · Answer

Yes. That makes sense. Thanks!

anonymous · Answer

Do you need help with the next few or do you understand now?