If sin(x) = 1/5 and x terminates in the first quadrant, determine cos2x
a) 2/5
b) 23/25
c) 24/25
d) 4/5

The correct answer for this question is letter B. 23/25.

This can be solved by doing the solution below.

sin(x) = opposite / hypotenuse
opposite = 1
hypotenuse = 5
adj^2 = hypotenuse^2 - opposite^2
adj^2 = 5^2 - 1^2
adj^2 = 25 - 1
adj^2 = √24 = 2√6
sin(x) = 1/5
cos(x) = adj/hyp = √24 / 5
tan(x) = opp/adj = 1 / √24

cos(2x) = cos^2(x) - sin^2(x) 
. . . . . . . = (√24/5)^2 - (1/5)^2 
. . . . . . . = 24/25 - 1/25
. . . . . . . = 23/25