Given an angle of $frac{5pi}{6}$ radians, find the coordinates of the point on the unit circle corresponding to this angle.
Answer 1
Lily Perez
Given an angle of $\frac{5\pi}{6}$ radians, we need to find the coordinates of the point on the unit circle corresponding to this angle.
First, note that $\frac{5\pi}{6}$ radians lies in the second quadrant. The reference angle for $\frac{5\pi}{6}$ is $\pi – \frac{5\pi}{6} = \frac{\pi}{6}$.
The coordinates of the point corresponding to $\frac{\pi}{6}$ on the unit circle are $(\cos(\frac{\pi}{6}), \sin(\frac{\pi}{6})) = (\frac{\sqrt{3}}{2}, \frac{1}{2})$.
Since $\frac{5\pi}{6}$ is in the second quadrant, the x-coordinate is negative and the y-coordinate is positive. Thus, the coordinates of the point are $(-\frac{\sqrt{3}}{2}, \frac{1}{2})$.
Answer 2
Charlotte Davis
To find the coordinates of the point on the unit circle corresponding to $frac{5pi}{6}$ radians:
1. Identify the reference angle: $pi – frac{5pi}{6} = frac{pi}{6}$.
2. The coordinates of $frac{pi}{6}$ are $(cos(frac{pi}{6}), sin(frac{pi}{6}))$ which equals $(frac{sqrt{3}}{2}, frac{1}{2})$.
3. Since $frac{5pi}{6}$ lies in the second quadrant, negate the x-coordinate: $(-frac{sqrt{3}}{2}, frac{1}{2})$.
Answer 3
James Taylor
The coordinates of $frac{5pi}{6}$ radians on the unit circle are found by using the reference angle $frac{pi}{6}$ and placing it in the second quadrant:
$(-frac{sqrt{3}}{2}, frac{1}{2})$
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