Find the exact values of $ sin $, $ cos $, and $ an $ at $ 30^{circ} $ on the unit circle
Answer 1
Abigail Nelson
First, we need to convert $ 30^{\circ} $ to radians:
$ 30^{\circ} = \frac{\pi}{6} $
Using the unit circle, the coordinates for $ \frac{\pi}{6} $ are $ \left( \frac{\sqrt{3}}{2}, \frac{1}{2} \right) $
From this, we can find:
$ \sin \frac{\pi}{6} = \frac{1}{2} $
$ \cos \frac{\pi}{6} = \frac{\sqrt{3}}{2} $
$ \tan \frac{\pi}{6} = \frac{\sin \frac{\pi}{6}}{\cos \frac{\pi}{6}} = \frac{\frac{1}{2}}{\frac{\sqrt{3}}{2}} = \frac{1}{\sqrt{3}} = \frac{\sqrt{3}}{3} $
Answer 2
Ava Martin
Convert $ 30^{circ} $ to radians:
$ 30^{circ} = frac{pi}{6} $
The coordinates for $ frac{pi}{6} $ on the unit circle are $ left( frac{sqrt{3}}{2}, frac{1}{2}
ight) $
Thus:
$ sin frac{pi}{6} = frac{1}{2} $
$ cos frac{pi}{6} = frac{sqrt{3}}{2} $
$ an frac{pi}{6} = frac{sqrt{3}}{3} $
Answer 3
Henry Green
Convert $ 30^{circ} $ to radians:
$ 30^{circ} = frac{pi}{6} $
Coordinates for $ frac{pi}{6} $ are $ left( frac{sqrt{3}}{2}, frac{1}{2}
ight) $
So:
$ sin frac{pi}{6} = frac{1}{2} $
$ cos frac{pi}{6} = frac{sqrt{3}}{2} $
$ an frac{pi}{6} = frac{sqrt{3}}{3} $
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