Note that normally we take t ≥ 0. For this sort of example, we must use radians for the angle.
`R=sqrt(12^2+5^2)=13` and `alpha=arctan(5/12)=0.39479`.
So `12\ sin t+5\ cos t=` `13\ sin(t+0.39479)`
So we can see that the amplitude is 13 A and this is the maximum value.
To find the first time that it occurs, we need to solve
Now sin θ = 1 for the first time when `theta=pi/2`. So we need to solve:
So the maximum value of 13 A will first occur at time t = 1.176 s.
We can see that this is correct from the graph:
`i=12\ sin t+5\ cos t`