Find the coordinates of the point on the unit circle where the angle with the positive $x$-axis is $frac{pi}{3}$
Answer 1
Amelia Mitchell
The unit circle is defined as a circle with radius 1 centered at the origin. The coordinates of any point on the unit circle can be given by $(\cos(\theta), \sin(\theta))$ where $\theta$ is the angle with the positive $x$-axis.
Given that $\theta = \frac{\pi}{3}$:
$\cos\left(\frac{\pi}{3}\right) = \frac{1}{2}$
$\sin\left(\frac{\pi}{3}\right) = \frac{\sqrt{3}}{2}$
Thus, the coordinates are:
$\left(\frac{1}{2}, \frac{\sqrt{3}}{2}\right)$
Answer 2
Alex Thompson
On the unit circle, the coordinates for an angle of $ heta$ are $(cos( heta), sin( heta))$.
For $ heta = frac{pi}{3}$, we find:
$cosleft(frac{pi}{3}
ight) = frac{1}{2}$
$sinleft(frac{pi}{3}
ight) = frac{sqrt{3}}{2}$
The coordinates are:
$left(frac{1}{2}, frac{sqrt{3}}{2}
ight)$
Answer 3
William King
The coordinates on the unit circle at $ heta = frac{pi}{3}$ are:
$left(frac{1}{2}, frac{sqrt{3}}{2}
ight)$
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