Where Do We Use This: Homework Statement

[Endorser]

Homework Statement

I have an assignment that is based on the forumal

A sin x + B cos x = K sin(x+ φ).

I need to: 1.Explain why we might need such a formula
2. Show proof or dervivation of this formula on which you add in english the
reasons for each step. (I know how to go from A sin x + B cos x to K sin(x+ φ))
3.Describe a real application of this formula

Homework Equations

A sin x + B cos x = K (sin x cos φ + cos x sin φ) = K sin(x+ φ).

The Attempt at a Solution

I have done a lot of searching and have come up with nothing...
Any help is appreciated

Thanks

 

[Mindscrape]

You probably ought to explicitly say the relation between A and B to K and Phi.

This kind of formula is mostly used for simple harmonic motion: if you have a mass on a spring or a pendulum swinging at small angles. It's actually more typical to see the formula as a cos argument rather than a sine.

 

[Endorser]

You probably ought to explicitly say the relation between A and B to K and Phi.

Could you explain to me what relation they hold ?

 

[Mindscrape]

A = K cos φ
B = K sin φ

comes directly from your second equation, the one with the trig identity.