Prove that $ sin(frac{pi}{6}) $ using the unit circle
Answer 1
Samuel Scott
To prove that $ \sin(\frac{\pi}{6}) $ using the unit circle, we start by locating the angle $ \frac{\pi}{6} $ on the unit circle.
The angle $ \frac{\pi}{6} $ corresponds to 30 degrees.
Using the unit circle, we see that the coordinates for this angle are $ (\frac{\sqrt{3}}{2}, \frac{1}{2}) $.
Since the sine of an angle is the y-coordinate on the unit circle, we have:
$ \sin(\frac{\pi}{6}) = \frac{1}{2} $
Answer 2
William King
To demonstrate that $ sin(frac{5pi}{6}) $ using the unit circle, locate the angle $ frac{5pi}{6} $ on the unit circle.
The angle $ frac{5pi}{6} $ corresponds to 150 degrees.
Using the unit circle, the coordinates for this angle are $ (-frac{sqrt{3}}{2}, frac{1}{2}) $.
Since the sine of an angle is the y-coordinate on the unit circle, we have:
$ sin(frac{5pi}{6}) = frac{1}{2} $
Answer 3
Isabella Walker
To find $ sin(frac{3pi}{4}) $ using the unit circle, locate the angle $ frac{3pi}{4} $ on the unit circle.
The angle $ frac{3pi}{4} $ corresponds to 135 degrees.
Using the unit circle, the coordinates for this angle are $ (-frac{sqrt{2}}{2}, frac{sqrt{2}}{2}) $.
The sine of an angle is the y-coordinate on the unit circle, so:
$ sin(frac{3pi}{4}) = frac{sqrt{2}}{2} $
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