Question

angle 0 is in quadrant 1 with sin0 = 2/5. Use the Pythagorean identity, sin^2 0 + cos^2 0 = 1, to calculate the value of cos0 as a radical.

Answer 1

We know that
sin²x+cos²x=1
so 
clear cos x
cos x=(+/-)√[1-sin²x]

in this problem
Angle 0 is in quadrant 1 -----> cos o and sin o are positive
sin o=2/5
cos x=√[1-(2/5)²]----> cos o=√[1-4/25]----> cos o=√[21/25]---> cos o=√21/5

the answer is
cos o=√21/5