Determine the coordinates of a point on the unit circle given a specific angle.
Answer 1
James Taylor
Given an angle \( \theta = \frac{5\pi}{6} \), find the coordinates of the corresponding point on the unit circle.
1. The angle \( \frac{5\pi}{6} \) is in the second quadrant where sine is positive and cosine is negative.
2. Using the unit circle, the coordinates for \( \theta = \frac{5\pi}{6} \) can be found using the reference angle \( \pi – \frac{5\pi}{6} = \frac{\pi}{6} \).
3. The coordinates for \( \frac{\pi}{6} \) are \( \left( \frac{\sqrt{3}}{2}, \frac{1}{2} \right) \).
4. Since \( \frac{5\pi}{6} \) is in the second quadrant, the x-coordinate will be negative.
Hence, the coordinates are $\left( -\frac{\sqrt{3}}{2}, \frac{1}{2} \right)$.
Answer 2
Lily Perez
Given an angle ( heta = frac{5pi}{6} ), find the coordinates of the corresponding point on the unit circle.
1. The angle ( frac{5pi}{6} ) is in the second quadrant where sine is positive and cosine is negative.
2. Using the unit circle, the coordinates for ( heta = frac{5pi}{6} ) can be found using the reference angle ( pi – frac{5pi}{6} = frac{pi}{6} ).
3. The coordinates for ( frac{pi}{6} ) are ( left( frac{sqrt{3}}{2}, frac{1}{2}
ight) ).
Therefore, the coordinates are $left( -frac{sqrt{3}}{2}, frac{1}{2}
ight)$.
Answer 3
John Anderson
Given an angle ( heta = frac{5pi}{6} ), the coordinates on the unit circle are $left( -frac{sqrt{3}}{2}, frac{1}{2}
ight)$.
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