Find the exact coordinates of the point where the angle $ frac{7pi}{6} $ intersects the unit circle
Answer 1
Thomas Walker
To find the coordinates of the point where the angle $ \frac{7\pi}{6} $ intersects the unit circle, we first identify the reference angle. The reference angle for $ \frac{7\pi}{6} $ is $ \frac{\pi}{6} $.
The coordinates for the angle $ \frac{\pi}{6} $ on the unit circle are $ \left( \frac{\sqrt{3}}{2}, \frac{1}{2} \right) $.
Since $ \frac{7\pi}{6} $ is in the third quadrant, both x and y coordinates will be negative:
$ \left( -\frac{\sqrt{3}}{2}, -\frac{1}{2} \right) $
Therefore, the coordinates are $ \left( -\frac{\sqrt{3}}{2}, -\frac{1}{2} \right) $.
Answer 2
Alex Thompson
To find the coordinates of the point where the angle $ frac{7pi}{6} $ intersects the unit circle, we observe that:
The reference angle is $ frac{pi}{6} $.
The coordinates for $ frac{pi}{6} $ are $ left( frac{sqrt{3}}{2}, frac{1}{2}
ight) $.
Since $ frac{7pi}{6} $ lies in the third quadrant, both values are negative:
$ left( -frac{sqrt{3}}{2}, -frac{1}{2}
ight) $
Answer 3
Abigail Nelson
The coordinates for the angle $ frac{7pi}{6} $ are:
$ left( -frac{sqrt{3}}{2}, -frac{1}{2}
ight) $
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