write an equation expressing 19cos(theta-50degrees) as a sum of sine and cosine.

Answer 1

Using the identity cos(a-b) = cos a cos b + sin a sin b

cos(θ-50) = cosθcos50 + sinθsin50
= .64cosθ + .77sinθ

so,

19cos(θ-50) = 19(.64cosθ + .77sinθ)
= 12.16cosθ + 14.63sinθ