7.4:Multiple-Angle Formulas

7.4: Multiple-Angle Formulas
Hi! In this chapter we mostly just derived a bunch of new identites (below). Hope it's helpful.

Double Angle Identities:

This identity is derived using an addition formula (sin(x+y)=sinxcosy+cosxsiny).

Like the identity above, this one also uses an addition formula.

To derive this identity, we used the formula from #2 and substituted in one minus cosine theta squared in place of sine theta squared (trigonometric identity).

We derived this identity using the addition formula for tangents.

 Power Reducing Identities:


1. To derive this identity, we used a previous identity that had sine squared in it, we then solved for sine squared.
2. This one is very similar to the first but with cosine instead.
3. For tangent squared, we substituted in equations equal to sine squared over cosine squared.

Half-Angle Identities:


1. To verify this identity we substituted u in for two theta.
2. (typo- last line should be: cos(u/2)=+/- V(1+cosu)/2 )
3. Solved by putting the identity we solved for sin(u/2) over the identity for cos(u/2).

Identities!!