Question

Express the function as a single sinusoid and hence find the amplitude and phase
f(x) = 3sinx-2cosx
@mathematics

Answer 1

Knowing how to do this is quite useful and important. There's a good exposition of around 10 minutes on the general identity starting at exactly 7:30 in this video:
http://ocw.mit.edu/courses/mathematics/18-03-differential-equations-spring-2010/video-lectures/lecture-8-continuation/
There's some other stuff in that 10 minutes as well, but no harm done.

For the record
\[ a \cos \theta + b \sin \theta = \sqrt{a^2 + b^2} \cos(\theta - \phi) \]
where
\[ \tan \phi = b/a \]

Answer 2

(The proof of the result begins at 13:30)

Answer 3

ah thanks i have that video on my computer already, have you ever noticed how good Arthur Mattuck is at black board camouflage