Trig Math Problem (Co-function identity)?

Hello,

sin[(π/2) - θ] = - 3/5

π < θ < (3π)/2

let's apply the co-function identity sin[(π/2) - θ] = cosθ:

cosθ = - 3/5

hence:

secθ = 1 /cosθ = - 5/3

let's find out tanθ applying the identity tanθ = ± √(sec²θ - 1):

tanθ = ± √(sec²θ - 1) = ± √[(- 5/3)² - 1] = ± √[(25/9) - 1] = ± √[(25 - 9)/9] =

± √(16/9) =

± 4/3

since θ lies in the third quadrant and therefore tanθ is positive, let's choose the plus sign, ending with:

tanθ = 4/3

I hope it's helpful