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
PB
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