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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

Answered by Prashan B. • Maths tutor

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