Determining the Position of (-frac{pi}{2}) on a Unit Circle
Answer 1
John Anderson
First, we recognize that the unit circle is a circle with a radius of 1 centered at the origin (0, 0) in the Cartesian coordinate system. The angle \(-\frac{\pi}{2}\) radians corresponds to a rotation in the clockwise direction from the positive x-axis.
Since \(\frac{\pi}{2}\) radians corresponds to 90 degrees, \(-\frac{\pi}{2}\) represents a rotation of 90 degrees clockwise. On the unit circle, rotating 90 degrees clockwise from the positive x-axis brings us to the negative y-axis.
Therefore, the coordinates on the unit circle at \(-\frac{\pi}{2}\) are:
$ (0, -1) $
Answer 2
Lucas Brown
To locate (-frac{pi}{2}) on the unit circle, we start with understanding the definition of the angle. The unit circle allows us to measure angles in radians, where (2pi) radians is a full circle.
The angle (-frac{pi}{2}) indicates a rotation of 90 degrees in the clockwise direction. Starting from the positive x-axis (0 degrees), moving 90 degrees clockwise lands us on the negative y-axis.
The coordinates corresponding to (-frac{pi}{2}) on the unit circle are represented by:
$ (0, -1) $
Answer 3
Lily Perez
On the unit circle, (-frac{pi}{2}) radians is equivalent to a 90-degree clockwise rotation from the positive x-axis.
Thus, the coordinates for (-frac{pi}{2}) are:
$ (0, -1) $
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