Determine the coordinates of points on the unit circle at specific angles

The unit circle is the circle of radius 1 centered at the origin (0, 0) in the coordinate plane. The coordinates of any point on the unit circle can be determined using trigonometric functions, specifically sine and cosine.

Given an angle $\theta$, the coordinates of the point on the unit circle are:

$ (\cos(\theta), \sin(\theta)) $

For example, for an angle $\theta = 0$, the coordinates are:

$ (\cos(0), \sin(0)) = (1, 0) $

For an angle $\theta = \frac{\pi}{2}$, the coordinates are:

$ (\cos(\frac{\pi}{2}), \sin(\frac{\pi}{2})) = (0, 1) $

Lastly, for an angle $\theta = \pi$, the coordinates are:

$ (\cos(\pi), \sin(\pi)) = (-1, 0) $

The unit circle has a radius of 1 and is centered at the origin. Points on this circle can be found using trigonometric functions.

For any angle $ heta$, the coordinates on the unit circle are:

$ (cos( heta), sin( heta)) $

For instance, at $ heta = 0$:

$ (1, 0) $

At $ heta = frac{pi}{2}$:

$ (0, 1) $

At $ heta = pi$:

$ (-1, 0) $

Use the unit circle formulas to find the points at given angles $ heta$.

For $ heta = 0$:

$ (1, 0) $

For $ heta = frac{pi}{2}$:

$ (0, 1) $

For $ heta = pi$:

$ (-1, 0) $

Start Using PopAi Today