Compound Angle Derivation

This PPT is a proof-almost-without-words of the compound angle formulae for sine, cosine, tangent.

You might use it to introduce the formulae.

I would recommend doing a starter activity before-hand where students have to find the opposite and adjacent sides of a triangle given the hypotenuse and the angle.

Why not also throw in a mechanics question like: write down the components of the 10N force which acts on the particle at 30 degrees above the horizontal, say. (Cue discussion about defining their own x and y directions.)

You can elicit all the side lengths before they appear on the screen. Then when all the lengths are shown (when it moves up to the top of the screen), you can get them to make a neat copy and write down equations for sin (a+b) and cos (a+b). Try tan if they are confident.