how do i use Pythagorean identity to find the exact coordinates of the point that has cos theta = 4/5
cos θ = 4/5 = x/r
We need to find y .....so we have
x^2 + y ^2 = r^2
4^2 + y^2 = 5^2
16 + y^2 = 25 subtract 16 from both sides
y^2 = 9 take ± roots
y = ± 3
Since the cosine is positive in two quadrants,....we have two possible points....in the first quadrant we have (4,3)......in the fourth quadrant we have (4, -3)