Find the sine, cosine, and tangent of $frac{pi}{6}$ on the unit circle.
Answer 1
Sophia Williams
To find the sine, cosine, and tangent of $\frac{\pi}{6}$, we use the unit circle values:
Sine of $\frac{\pi}{6}$: $\sin\left(\frac{\pi}{6}\right) = \frac{1}{2}$
Cosine of $\frac{\pi}{6}$: $\cos\left(\frac{\pi}{6}\right) = \frac{\sqrt{3}}{2}$
Tangent of $\frac{\pi}{6}$: $\tan\left(\frac{\pi}{6}\right) = \frac{\sin\left(\frac{\pi}{6}\right)}{\cos\left(\frac{\pi}{6}\right)} = \frac{1/2}{\sqrt{3}/2} = \frac{1}{\sqrt{3}} = \frac{\sqrt{3}}{3}$
Answer 2
James Taylor
Given $ heta = frac{pi}{6}$, let us find the trigonometric values on the unit circle:
$sin heta = sinleft(frac{pi}{6}
ight) = frac{1}{2}$
$cos heta = cosleft(frac{pi}{6}
ight) = frac{sqrt{3}}{2}$
$ an heta = anleft(frac{pi}{6}
ight) = frac{sinleft(frac{pi}{6}
ight)}{cosleft(frac{pi}{6}
ight)} = frac{frac{1}{2}}{frac{sqrt{3}}{2}} = frac{1}{sqrt{3}} = frac{sqrt{3}}{3}$
Answer 3
Michael Moore
For $ heta = frac{pi}{6}$ on the unit circle:
Sine: $sinleft(frac{pi}{6}
ight) = frac{1}{2}$
Cosine: $cosleft(frac{pi}{6}
ight) = frac{sqrt{3}}{2}$
Tangent: $ anleft(frac{pi}{6}
ight) = frac{sinleft(frac{pi}{6}
ight)}{cosleft(frac{pi}{6}
ight)} = frac{1}{sqrt{3}} = frac{sqrt{3}}{3}$
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