We find α using

`a=text(arctan)a/b`

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

`R=sqrt(a^2+b^2)`

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:

cosine combined

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).