If in doubt, \(k\cos (x - \alpha )\) usually works ... You've been given the form to write the equation in, so now equate both expressions. This just means, make them equal each other.

Note: This only works when \(x\) is measured in radians. We are now going to look at more complex trigonometric functions where we will use the general rule: \(\int {\cos (ax + b)dx = \frac{1} ...