Compound Angle Identities/Formulae

Compound Angle Identities/Formulae

These formulae help us simplify some calculations, and further, help us to prove more complicated trig identities. For now, you will be given the identities, but later in the unit you will be doing an independent investigation to prove these.

Sine Identities:

Cosine Identities:

We can apply the compound angle formulae to determine exact trig ratios for angles that can be expressed as sums or differences of special angles .

Ex. Show that is true for and .

Ex2. Show that is true for and .

Ex3. Use an appropriate compound angle formula to determine the exact value of .

***Note: What we need to do here is represent the angle as a sum or difference of two of the special angles . Remember, we also know all the ratios when any of these special angles are the related acute angle ex.