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

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Answer 1 · 2016-05-06T05:17:29

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

$f(t)= 5 sin t + 12 cos t$ . 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 $2pi$ ..

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