# Exponential function

## Homework Statement

This topic is under linear system differential equation.Solve the system by using exponential method. Just want to ask the expansion of exponential function

## Homework Equations

e^x=1+x+(x^2)/2!+(x^3)/3!+........

## The Attempt at a Solution

Besides what is the function of sin x and cos x in continued function (such in e^x)?
Thanks!

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## The Attempt at a Solution

Besides what is the function of sin x and cos x in continued function (such in e^x)?
Thanks!
I'm not really for sure what your question even is. What problem are you trying to solve? Are you asking for the power series for sine and cosine?
\begin{align*} \sin x &= x - \frac{x^3}{3!} + \frac{x^5}{5!} - \frac{x^7}{7!} + \cdots \\ \cos x &= 1 - \frac{x^2}{2!} + \frac{x^4}{4!} - \frac{x^6}{6!} + \cdots \end{align*}

Or are you asking for the following identities?
\begin{align*} \sin x &= \frac{e^{ix}-e^{-ix}}{2i} \\ \cos x &= \frac{e^{ix} + e^{-ix}}{2} \end{align*}

Mark44
Mentor

## Homework Statement

This topic is under linear system differential equation.Solve the system by using exponential method. Just want to ask the expansion of exponential function

## Homework Equations

e^x=1+x+(x^2)/2!+(x^3)/3!+........