I dont know how to solve these trig problems

Question

if sin(pi/11) = cos(theta) and 0 < theta <pi/2 , then

The answer needs to be in radians no decimals. I don't see an explanation of how to do this in my lecture or textbook

Answer 1

sine and cosine are complimentary:

sin(β) = cos(π/2 - β)

or if β = π/11

cos(π/2 - π/11) = sin(π/11) = cos(θ)

So θ = π/2 - π/11 = (11π-2π)/22 = 9π/22 radians