Given sin x=5/13 and 0<= x <= π/2 find:

Question

a) sin 2x

b) cos 2x

c) tan 2x

Answer 1

you have a 5-12-13 triangle, so
cosx = 12/13
tanx = 5/12
Now just use your double angle formulas. For instance,
tan 2x = 2tanx/(1-tan^2 x) = 2(5/12)/(1 - (5/12)^2) = 120/119