The point P is on the unit circle. If the y-coordinate of P is 5/7 and P is in the quadrant II, find the x-coordinate.

Answer 1

Any point on the unit circle is given as (cos θ,sin θ), where θ is the angle from the positive x-axis. Since the y-coordinate is 5/7, we know the point has to be in the first or second quadrant, and that the x-coordinate for the point in the second quadrant is simply the negation of the x-coordinate for the point if it were in the first quadrant. Now since we have sin θ=5/7, then θ=arcsin(5/7). So the x-coordinate we need (find by entering into a calculator) is -cos(arcsin(5/7))=-2√(6)/7≈-0.7

Answer 2

Mark is, as usual, correct!

However algebraically:

The equation of the unit circle is x² + y² = 1

If you substitute y=5/7, you will get two possible values, only one of which is correect.