Find the amplitude of Find the amplitude of 4 sin2t 7 cos2t

Find the amplitude of

Solution

Let 4sin(2t) + 7cos(2t) = k cos ( 2t - ) for k > 0
4sin(2t) + 7cos(2t) = (k cos ) cos 2t + (k sin ) sin 2t

We findd : 4 = k cos and 7 = k sin

square both and then add :

k^2(sin² + cos² ) = 4^2 + 7^2
k^2(sin² + cos² ) = 16 + 49

k^2 = 65
hence amplitude k = 65


Amplitude is k = 25