Find the coordinates of point on the unit circle

Given a point $(x, y)$ on the unit circle, we know that the equation of the circle is:

$ x^2 + y^2 = 1 $

If $ x = \frac{1}{2} $, then we can find $ y $ by solving:

$ (\frac{1}{2})^2 + y^2 = 1 $

$ \frac{1}{4} + y^2 = 1 $

Solving for $ y $:

$ y^2 = 1 – \frac{1}{4} $

$ y^2 = \frac{3}{4} $

$ y = \pm \frac{\sqrt{3}}{2} $

So the coordinates are:

$ ( \frac{1}{2}, \frac{\sqrt{3}}{2} ) $ or $ ( \frac{1}{2}, -\frac{\sqrt{3}}{2} ) $

Given $ x = frac{1}{2} $ on the unit circle:

$ x^2 + y^2 = 1 $

$ (frac{1}{2})^2 + y^2 = 1 $

$ frac{1}{4} + y^2 = 1 $

$ y^2 = 1 – frac{1}{4} $

$ y^2 = frac{3}{4} $

$ y = pm frac{sqrt{3}}{2} $

Coordinates: $ ( frac{1}{2}, frac{sqrt{3}}{2} ) $ and $ ( frac{1}{2}, -frac{sqrt{3}}{2} ) $

For $ x = frac{1}{2} $ on unit circle:

$ x^2 + y^2 = 1 $

$ frac{1}{2} $ yields $ y = pm frac{sqrt{3}}{2} $

Coordinates: $ ( frac{1}{2}, frac{sqrt{3}}{2} ) $, $ ( frac{1}{2}, -frac{sqrt{3}}{2} ) $

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