Question

Develop the Maclaurin series for: v=f(x)=sinx

Answer 1

very famous series, a good one to memorize

Answer 2

\(\sin(0)=0\) so there is no constant
\(\cos(0)=1\) so first term is \(x\)
\(-\sin(0)=0\) so no \(x^2\) term
\(-\cos(0)=-1\) so cube term is \(\frac{x^3}{3!}\)
\(\sin(0)=0\) still so no \(x^4\) term
now it repeats

Answer 3

start with
\[x-\frac{x^3}{3!}+\frac{x^5}{5!}-\frac{x^7}{7!}+...\]

Answer 4

only odd powers, as sine is an odd function

Answer 5

thank you!

Answer 6

yw

Answer 7

really, memorize it, it comes up again and again
also memorize one for cosine
both are easy to remember

Answer 8

I will now. We went through the whole chapter in one day, it went by so fast that only the prof got it lol