Question

If the point P(-3/5, y) lies on the unit circle and P is in the third quadrant, what does y equal?

Answer 1

If the point P(-3/5, y) lies on the unit circle, then we know that:

x^2 + y^2 = 1

Substituting x = -3/5, we get:

(-3/5)^2 + y^2 = 1

9/25 + y^2 = 1

y^2 = 1 - 9/25

y^2 = 16/25

Taking the square root of both sides, we get:

y = ±4/5

Since P is in the third quadrant (i.e., x is negative and y is negative), y must be negative. Therefore, y = -4/5.