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

Ebone6v

Ebone6v

Answered question

2022-08-10

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

Answer & Explanation

Brooks Hogan

Brooks Hogan

Beginner2022-08-11Added 18 answers

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 cos t )
= 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 2 π

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