Find the angle corresponding to the point $ left( frac{1}{2}, -frac{sqrt{3}}{2}
ight) $ on the unit circle.
Answer 1
Amelia Mitchell
To find the angle that corresponds to the point $ \left( \frac{1}{2}, -\frac{\sqrt{3}}{2} \right) $ on the unit circle, we look at the coordinates.
The x-coordinate is $ \frac{1}{2} $ and the y-coordinate is $ -\frac{\sqrt{3}}{2} $. These values correspond to an angle in the fourth quadrant.
The reference angle with these coordinates is $ \frac{\pi}{3} $ because:
$ \cos \theta = \frac{1}{2} \text{ and } \sin \theta = -\frac{\sqrt{3}}{2} $
Since the angle is in the fourth quadrant, the actual angle is:
$ \theta = 2\pi – \frac{\pi}{3} = \frac{5\pi}{3} $
Answer 2
Charlotte Davis
To find the angle corresponding to the point $ left( frac{1}{2}, -frac{sqrt{3}}{2}
ight) $ on the unit circle, we use the coordinates to determine the reference angle:
$ cos heta = frac{1}{2} ext{ and } sin heta = -frac{sqrt{3}}{2} $
These coordinates match the reference angle $ frac{pi}{3} $.
Since the point is in the fourth quadrant, the angle is:
$ heta = 2pi – frac{pi}{3} = frac{5pi}{3} $
Answer 3
Ava Martin
The coordinates $ left( frac{1}{2}, -frac{sqrt{3}}{2}
ight) $ correspond to:
$ heta = frac{5pi}{3} $
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