sin x = cos x??? co-functions?

Question

my teacher gave us a hw. explain how these r co-functions:
sin x = cos x
tan x= cot x

i thought it should be:
sin x = cos 90-x

so now im confused and don't know how to do?

can anybody explain sin x = cos x, please? or is it the teacher's mistake?

Answer 1

You're correct. Note, for the functions below, π/2 radians = 90 degrees.
sin x = cos (π/2 - x) and cos x = sin (π/2 - x)
tan x = cot (π/2 - x) and cot x = tan (π/2 - x)
sec x = csc (π/2 - x) and csc x = sec (π/2 - x).

Answer 2

They are equal at 45 degrees (pi/4) and at 225 degrees (5pi/4). if sin x = cos 90 - x, and sin x = cos x, then x = 90 - x, or x = 45. The same is true for 225, if you care to try.