Question

suppose sin(A) = 2/5. use the trig identity sin^2(A)+cos^2(A)=1 to find cos(A) in quadrant I. show all steps and round to ten-thousandth

Answer 1

In quadrant I, $\cos(A)$ is positive. So

$\sin^2(A) + \cos^2(A) = 1 \implies \cos(A) = \sqrt{1-\sin^2(A)} = \dfrac{\sqrt{21}}5 \approx \boxed{0.9165}$