Question

Given that sin^2x = 4/13, what is the cos^2x?
I am so lost. I need to show my work. Please help.
THANK YOU!

Answer 1

if sin^2 x = 4/13
sin x = ± 2/√13
telling me that x could in any of the 4 quadrants

using the first quadrant triangle
x^2 + 2^2 = √13^2
x^2 = 9
cos^2 = x^2/r^2 = 9/13

or, in a shorter way:

we know : sin^2 x + cos^2 x = 1
cos^2 x + 4/13 = 1
cos^2 x = 1-4/13 = 9/13