Find the sine, cosine, and tangent values for the angle $ heta = frac{5pi}{6}$ using the unit circle.
Answer 1
William King
For the angle $\theta = \frac{5\pi}{6}$:
The reference angle is $\pi – \frac{5\pi}{6} = \frac{\pi}{6}$.
In the second quadrant, sine is positive, cosine is negative, and tangent is negative.
Thus, the values are:
$\sin(\frac{5\pi}{6}) = \sin(\frac{\pi}{6}) = \frac{1}{2}$
$\cos(\frac{5\pi}{6}) = -\cos(\frac{\pi}{6}) = -\frac{\sqrt{3}}{2}$
$\tan(\frac{5\pi}{6}) = \frac{\sin(\frac{5\pi}{6})}{\cos(\frac{5\pi}{6})} = \frac{\frac{1}{2}}{-\frac{\sqrt{3}}{2}} = -\frac{1}{\sqrt{3}} = -\frac{\sqrt{3}}{3}$
Answer 2
Amelia Mitchell
To determine the sine, cosine, and tangent of $ heta = frac{5pi}{6}$:
First, find the reference angle $pi – frac{5pi}{6}$, which equals $frac{pi}{6}$.
Given the quadrant, sine remains positive while cosine and tangent become negative:
$sin(frac{5pi}{6}) = frac{1}{2}$
$cos(frac{5pi}{6}) = -frac{sqrt{3}}{2}$
$ an(frac{5pi}{6}) = -frac{1}{sqrt{3}} = -frac{sqrt{3}}{3}$
Answer 3
Abigail Nelson
For $ heta = frac{5pi}{6}$, the reference angle is $frac{pi}{6}$:
$sin(frac{5pi}{6}) = frac{1}{2}$
$cos(frac{5pi}{6}) = -frac{sqrt{3}}{2}$
$ an(frac{5pi}{6}) = -frac{sqrt{3}}{3}$
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