We find α using

Once again, α has to be in radians for this example.

Since a = 2.348 and b = 1.251, we have:

α = arctan (2.348/1.251) = 1.081

We find R using

So R = √ (2.348² + 1.251²) = 2.660

So we can write:

2.340 sin θ − 1.251 cos θ = -2.660 cos (θ + 1.081)

Checking using a graph, we obtain the following for each side of our answer:

We see that our negative cosine curve has an amplitude of 2.660 and it has been shifted to the left by 1.081 radians, which is consistent with the expression -2.660 cos (θ + 1.081).