Question

Can someone help me with this ? Find the missing coordinate of P, using the fact that P lies on the unit circle in the given quadrant.
P(-7/25, ???), quadrant II: ...?

Answer 1

What we can use here is the pythagorean theorem and you will see how can we solev this. You are given the x value and you also know that the equation of the circle can be written as x^2 + y^2 = r^2. Since this is a unit circle the equation that you are going to get is x^2 + y^2 = 1.
This equation describes your circle. Now put in the x value that you have:
(7/25)^2 + y^2 = 1
 and now rearrange the equation to solve for y.
 y^2 = 1 - (7/25)^2
 And then y = SQRT ( 1 - (7/25)^2 )
 So if you square root it you will get a positive and a negative answer.Hence, you select a positive answer from your square root. Because we know that, since it is specified that the answer must lie in the second quadrant, then you know it has to be in the quadrant that has -x and a positive y.