What are the coordinates of the point on the unit circle at an angle of $frac{pi}{3}$ radians?
Answer 1
Benjamin Clark
Given an angle of $\frac{\pi}{3}$ radians, we want to find the coordinates of the corresponding point on the unit circle.
The unit circle has a radius of 1, and the coordinates of any point on the unit circle can be found using the cosine and sine of the angle.
Therefore, the x-coordinate is $\cos(\frac{\pi}{3})$ and the y-coordinate is $\sin(\frac{\pi}{3})$.
We know from trigonometric values:
$\cos(\frac{\pi}{3}) = \frac{1}{2}$
$\sin(\frac{\pi}{3}) = \frac{\sqrt{3}}{2}$
Thus, the coordinates are:
$(\frac{1}{2}, \frac{\sqrt{3}}{2})$
Answer 2
Matthew Carter
To find the coordinates of the point on the unit circle at an angle of $frac{pi}{3}$ radians, we use the unit circle definitions.
The unit circle has a radius of 1. For an angle $ heta$, the coordinates are $(cos( heta), sin( heta))$.
Here, $ heta = frac{pi}{3}$.
So, $cos(frac{pi}{3}) = frac{1}{2}$ and $sin(frac{pi}{3}) = frac{sqrt{3}}{2}$.
Therefore, the coordinates are:
$(frac{1}{2}, frac{sqrt{3}}{2})$
Answer 3
Mia Harris
To find the coordinates at $frac{pi}{3}$ radians on the unit circle:
$cos(frac{pi}{3}) = frac{1}{2}$ and $sin(frac{pi}{3}) = frac{sqrt{3}}{2}$.
Thus, coordinates are $(frac{1}{2}, frac{sqrt{3}}{2})$.
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