# Defining Exponential and Trigonometric Functions Using Differential Equations

@article{Diamond2014DefiningEA, title={Defining Exponential and Trigonometric Functions Using Differential Equations}, author={Harvey Diamond}, journal={Mathematics Magazine}, year={2014}, volume={87}, pages={37 - 42} }

Summary This note addresses the question of how to rigorously define the functions exp(x), sin(x), and cos(x), and develop their properties directly from that definition. We take a differential equations approach, defining each function as the solution of an initial value problem. Assuming only the basic existence/uniqueness theorem for solutions of linear differential equations, we derive the standard properties and identities associated with these functions. Our target audience is…

## One Citation

### Defining trigonometric functions via complex sequences

- MathematicsThe Mathematical Gazette
- 2016

In the literature we find several different ways of introducing elementary functions. For the exponential function, we mention the following ways of characterising the exponential function: (a) (b) ,…

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