Consider the trigonometric expression .

MATHEMATICS · Multi-part · AP · AP Precalculus · Trigonometric and Polar Functions · Trigonometric and Polar Functions

Problem

Consider the trigonometric expression

7\sin x-24\cos x

. (i) Define the term “amplitude” for an expression of the form

a\sin x+b\cos x

. State how it is obtained from the numerical coefficients

a

and

b

. (ii) Calculate the amplitude of

7\sin x-24\cos x

. (iii) Hence write down the maximum and minimum values that

7\sin x-24\cos x

can assume for all real

x

, and give a brief reason for your answer.