Find the sine and cosine of the angle $ heta$ when $ heta = frac{pi}{6}$.
Answer 1
Christopher Garcia
To find the sine and cosine of the angle $\theta$ when $\theta = \frac{\pi}{6}$, we can use the unit circle.
The angle $\frac{\pi}{6}$ radians corresponds to 30 degrees.
On the unit circle, the coordinates of the point at angle $\frac{\pi}{6}$ are:
$\left(\cos\left(\frac{\pi}{6}\right), \sin\left(\frac{\pi}{6}\right)\right)$
From trigonometric values:
$\cos\left(\frac{\pi}{6}\right) = \frac{\sqrt{3}}{2}$
$\sin\left(\frac{\pi}{6}\right) = \frac{1}{2}$
Therefore, the sine and cosine of the angle $\theta$ when $\theta = \frac{\pi}{6}$ are given by:
$\sin\left(\frac{\pi}{6}\right) = \frac{1}{2}$
$\cos\left(\frac{\pi}{6}\right) = \frac{\sqrt{3}}{2}$
Answer 2
Emily Hall
To determine $sinleft(frac{pi}{6}
ight)$ and $cosleft(frac{pi}{6}
ight)$:
On the unit circle, $frac{pi}{6}$ radians (30 degrees) has coordinates:
$left(cosleft(frac{pi}{6}
ight), sinleft(frac{pi}{6}
ight)
ight)$
We know:
$cosleft(frac{pi}{6}
ight) = frac{sqrt{3}}{2}$
$sinleft(frac{pi}{6}
ight) = frac{1}{2}$
Thus:
$sinleft(frac{pi}{6}
ight) = frac{1}{2}$
$cosleft(frac{pi}{6}
ight) = frac{sqrt{3}}{2}$
Answer 3
Maria Rodriguez
Using the unit circle, for $ heta = frac{pi}{6}$:
$cosleft(frac{pi}{6}
ight) = frac{sqrt{3}}{2}$
$sinleft(frac{pi}{6}
ight) = frac{1}{2}$
Therefore:
$sinleft(frac{pi}{6}
ight) = frac{1}{2}$
$cosleft(frac{pi}{6}
ight) = frac{sqrt{3}}{2}$
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