Calculate the coordinates of a point on the unit circle given the angle $ heta$

To find the coordinates of a point on the unit circle for a given angle $\theta$, use the following formulas:

$x = \cos(\theta)$

$y = \sin(\theta)$

For example, if $\theta = 45^\circ$:

$x = \cos(45^\circ) = \frac{\sqrt{2}}{2}$

$y = \sin(45^\circ) = \frac{\sqrt{2}}{2}$

So the coordinates are $\left( \frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2} \right)$.

To find the coordinates of a point on the unit circle for a given angle $ heta$, use these formulas:

$x = cos( heta)$

$y = sin( heta)$

For instance, if $ heta = 60^circ$:

$x = cos(60^circ) = frac{1}{2}$

$y = sin(60^circ) = frac{sqrt{3}}{2}$

The coordinates are $left( frac{1}{2}, frac{sqrt{3}}{2}
ight)$.

The coordinates of a point on the unit circle for angle $ heta$ are:

$x = cos( heta)$

$y = sin( heta)$

For $ heta = 90^circ$:

$x = cos(90^circ) = 0$

$y = sin(90^circ) = 1$

So the coordinates are $left(0, 1
ight)$.

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