Question

how do i find six trig functions for cos(pi over 2-x)=3/5, cos x=4/5?

Answer 1

given cos x = 4/5
by making a diagram, you should recognize the 3,4,5 right-angles triangle
secondly, the cosine is positive in quadrants I and IV

in I:
sinx = 3/5 , csc x = 5/3
cosx = 4/5 , sec x = 5/4
tanx = 4/3 , cot x = 3/4

you do IV


back to cos(pi over 2-x)=3/5
cos (π/2 - x) = 3/5
(cosπ/2)(cosx) + (sinπ/2)(sinx)= 3/5
sinx = 3/5
(hey, we knew that!)