How to Find a Missing Coordinate on a Unit Circle
If you have the value of one of a point’s coordinates on the unit circle and need to find the other, you can substitute the known value into the unitcircle equation and solve for the missing value.
You can choose any number between 1 and –1, because that’s how far the unit circle extends along the x and yaxes. For example, say 2/5 is the xcoordinate of a point on the unit circle. You can find the ycoordinate like so:

Substitute the xcoordinate value into the unitcircle equation.

Square the xcoordinate and subtract that value from each side.

Take the square root of each side.
Note that the ycoordinate can have two values, because the unit circle has two different points for every particular xcoordinate (and for every ycoordinate). You can see how that happens:
Another example: Find the xcoordinate (or coordinates) if the ycoordinate is –7/25.

Substitute the ycoordinate value into the unitcircle equation.

Square the ycoordinate and subtract that value from each side.

Take the square root of each side.
As you can see, the xcoordinate here has two values, and the two points are