Question

What is the maximum value of `5sin(t) + 12cos(t)`?

Answer 1

The maximum is 13 and minimum is `-13`.

Explanation:

`f(t)= 5 sin t + 12 cos t`. We can compound these two oscillations into a single sine oscillation.

`f(t) = 13((5/13) sin t + (12/13) cos t)`

`= 13 (cos b sin t + sin b cost )`

`= 13 sin ( t + b )`, where `sin b =12/13 and cos b = 5/13`.

So, `-13 <= f(t) = 13 sin ( t + b ) <=13`

The amplitude of the oscillation is 13 and the period is `2pi`..