Find the sine, cosine, and tangent values for the angle $frac{pi}{6}$ on the unit circle.
Answer 1
Sophia Williams
To solve this, we need to find the sine, cosine, and tangent values for the angle $\frac{\pi}{6}$ on the unit circle.
The angle $\frac{\pi}{6}$ corresponds to 30 degrees.
Using the unit circle, we know that:
$ \sin \left( \frac{\pi}{6} \right) = \frac{1}{2} $
$ \cos \left( \frac{\pi}{6} \right) = \frac{\sqrt{3}}{2} $
$ \tan \left( \frac{\pi}{6} \right) = \frac{ \sin \left( \frac{\pi}{6} \right) }{ \cos \left( \frac{\pi}{6} \right) } = \frac{\frac{1}{2}}{\frac{\sqrt{3}}{2}} = \frac{1}{\sqrt{3}} = \frac{\sqrt{3}}{3} $
So, the values are:
$ \sin \left( \frac{\pi}{6} \right) = \frac{1}{2} $
$ \cos \left( \frac{\pi}{6} \right) = \frac{\sqrt{3}}{2} $
$ \tan \left( \frac{\pi}{6} \right) = \frac{\sqrt{3}}{3} $
Answer 2
Abigail Nelson
Let’s find the sine, cosine, and tangent for the angle $frac{pi}{6}$ on the unit circle.
We know that $frac{pi}{6}$ is equal to 30 degrees.
From the unit circle properties:
$ sin left( frac{pi}{6}
ight) = frac{1}{2} $
$ cos left( frac{pi}{6}
ight) = frac{sqrt{3}}{2} $
We calculate the tangent:
$ an left( frac{pi}{6}
ight) = frac{ sin left( frac{pi}{6}
ight) }{ cos left( frac{pi}{6}
ight) } = frac{frac{1}{2}}{frac{sqrt{3}}{2}} = frac{1}{sqrt{3}} = frac{sqrt{3}}{3} $
Hence, we get:
$ sin left( frac{pi}{6}
ight) = frac{1}{2} $
$ cos left( frac{pi}{6}
ight) = frac{sqrt{3}}{2} $
$ an left( frac{pi}{6}
ight) = frac{sqrt{3}}{3} $
Answer 3
Thomas Walker
To find the sine, cosine, and tangent for $frac{pi}{6}$:
$ sin left( frac{pi}{6}
ight) = frac{1}{2} $
$ cos left( frac{pi}{6}
ight) = frac{sqrt{3}}{2} $
$ an left( frac{pi}{6}
ight) = frac{sqrt{3}}{3} $
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