Rewrite − 3 sin ( x ) + 4 cos ( x ) as A sin ( x + ϕ ) A = ϕ = Note: ϕ should be in the interval − π < ϕ < π

Answer 1

Multiply and divide by √[(-3)² + 4²] to get: 5[(-3/5)sinx + (4/5)cosx]

cosφ = -3/5 and sinφ = 4/5, where φ = Cos^-1(-3/5) = 2.21 radians

So, we have -3sinx + 4cosx = 5[sinxcosφ + cosxsinφ] = 5sin(x + φ) = 5sin(x + 2.21)