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=sqrt(2.348^2+ 1.251^2) = 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).