Thread: Solving for Theta in Sin(Theta)=1/2 Using The Unit Circle

1. Solving for Theta in Sin(Theta)=1/2 Using The Unit Circle

I've been using Brightstorm recently to prepare for the next lesson, it's great but occasionally you run into some questions and I don't believe they get answered any time soon.

I'm watching this video in particular and I am stuck with the second solution for $sin(theta)=1/2$
Solving Trigonometric Equations (Video)
(Picture)

If (pi) radians is equal to 180 degrees and all three angles of all three triangles is equal to 180 degrees, why isn't the supplement angle $(pi)-(2(theta))$?

2. not sure if this helps but if

$\sin{\theta} = \frac{1}{2}$
then

$\sin^{-1}{\left(\frac{1}{2}\right)} = \frac{\pi}{6}$ or $\frac{5\pi}{6}$

3. That is the result he also got using (pi) - (theta). However, for me, it visual doesn't make sense. The angle of the center triangle must (in my eyes at least) (pi) - (2theta). Is the supplementary angle different?

Edit: Looking at again, it looks like the second solution includes the first angle as well which would make sense. Now I don't understand the supplement angle. Checking Google as of now...

4. angle between

Originally Posted by Altermeris
That is the result he also got using (pi) - (theta). However, for me, it visual doesn't make sense. The angle of the center triangle must (in my eyes at least) (pi) - (2theta). Is the supplementary angle different?
by the angle of the center triangle do you mean the angle between $\frac{\pi}{6}$ and $\frac{5\pi}{6}$

if so then $\pi - 2\theta$will give the answer

however, I think supplement refers to pairs of angles between $\pi$

the center angle is not a supplement to $\theta$

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cos theta eauql

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