1. (a) Express 7cosx - 24sin x in the form R cos (x + a), (b) hence what is the minimum value of this equation

(a) Rcos (x+a) = Rcosxcosa - Rsinxsina

7cosx - 24sinx = Rcosxcosa - Rsinxsina

Rcosa = 7,    Rsina = 24

Tan a = 24/7

       a = 1.287 (3 S.F.)

R² = 24² + 7²

R = 25

Therefore 25cos(x + 1.287)

(b) minimum value = -1 * 25

                              = -25