Need help with some Precalc Trigonometry.

I have been trying to figure out how to do this problem almost all day, hopefully you guys can help. Here is the problem "find two angles between 0(degrees) and 360(degrees) which satisfy the following:

ex: sin(theta)= -1/2

please include work so i can do it by myself

Re: Need help with some Precalc Trigonometry.

First, ask yourself how many solutions will there be, and in which quadrants will they be. Think of where the line $\displaystyle y=-\frac{1}{2}$ will intersect the unit circle. Do you understand why this works?

Re: Need help with some Precalc Trigonometry.

No, sadly enough, i dont. But i know how to find out what quadrant it will be in, and thats about it, is there any way i could put a picture on here of the problem so you can see it or is that against the rules.

Re: Need help with some Precalc Trigonometry.

You may attach images here, without breaking any rules as long of course as the image does not contain anything inappropriate.

Imagine a ray which originates at the origin and terminates at some point on the unit circle. Now, imagine that this terminal point is initially at $\displaystyle (1,0)$. Then, let the ray move in a counter-clockwise direction to a particular point of interest on the unit circle. Let the angle through with the ray has turned be $\displaystyle \theta$. Then we have that the coordinates of the terminal point are $\displaystyle (\cos(\theta),\sin(\theta))$. Does this sound familiar?

Re: Need help with some Precalc Trigonometry.

my teacher hasn't taught us how to use the unit circle, but gave us an assignment(worth a quiz grade) with some questions on the problem i asked you, ill put up a picture of the problems one i tried to answer and i erased but i put(210, and 330) as the answer, i kind of under stand what you are talking about with the terminal point you showed me but i dont know how to use it.

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Re: Need help with some Precalc Trigonometry.

Attachment 25908

im going to sleep, so if i dont respond in a while, thats why. Thank you for helping me.

Re: Need help with some Precalc Trigonometry.

Well, there are certainly other ways of looking at it, and whatever way you used worked as you have the correct angles in degrees.

I suspect you observed that $\displaystyle \sin(30^{\circ})=\frac{1}{2}$, then used:

$\displaystyle (180+30)^{\circ}$ and $\displaystyle (360-30)^{\circ}$

Re: Need help with some Precalc Trigonometry.

Well, actually my sister help me use the unit circle and i was able to just find 1/2 on there and get 210 and 330, so all i really need to do is find the reference angle and minus 180 and 360 by it?