Question

How do you find the Maclaurin Series for `f(x)= sin(x+π)`?

Answer 1

`sin(x+pi) = -x+x^3/(3!)-x^5/(5!)+x^7/(7!)-...`

Explanation:

`f(x) = sin(x+ pi)`

Using the trig sum formula

`sin(A+B) -= sinAcosB+cosAsinB`

Then

`f(x) = sinxcospi+sinpicosx`
`:. f(x) = sinx(-1)+(0)cosx`
`:. f(x) = -sinx`

The Maclaurin Series for sinx is
`sinx=x-x^3/(3!)+x^5/(5!)-x^7/(7!)+...`

Hence,
`f(x) = -x+x^3/(3!)-x^5/(5!)+x^7/(7!)-...`