Where in trig are we taught Asin(θ+ø) = Bsinθ+Ccosθ?

[gikiian]

My undergrad senior-year Mechanical Vibrations book tells me that I should remember the notion that Asin(θ+ø) can also be represented in the form of Bsinθ+Ccosθ (and other linear combinations of sines and cosines), from high-school trigonometry class. However, I was never taught this in my high-school. I even read a lot of material and watched a lot of YouTube videos on trigonometry in my high-school years, but the notion that Asin(θ+ø) can also be represented in the form of Bsinθ+Ccosθ etc never came up.

I am just wondering where exactly in a average high-school curriculum are we taught this notion? Answer of one or two sentences would be enough.

 

[gopher_p]

It's the angle addition formula for sine; $$A\sin(\theta+\phi)=A\sin\theta\cos\phi+A\cos\theta\sin\phi=B\sin \theta +C\cos\theta$$ where $$B=A\cos\phi\text{ and } C=A\sin\phi$$

So I guess that exact formula maybe isn't something that you saw in trig, but it follows immediately from one that you most definitely should have seen.