Difference between revisions of "Sine"
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| + | <strong>Proposition:</strong> $\sin(x)=\displaystyle\sum_{k=0}^{\infty} \dfrac{(-1)^kx^{2k+1}}{(2k+1)!}$ | ||
| + | <div class="mw-collapsible-content"> | ||
| + | <strong>Proof:</strong> proof goes here █ | ||
| + | </div> | ||
| + | </div> | ||
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<strong>Proposition:</strong> $\sin(x) = x \displaystyle\prod_{k=1}^{\infty} \left( 1 - \dfrac{x^2}{k^2\pi^2} \right)$ | <strong>Proposition:</strong> $\sin(x) = x \displaystyle\prod_{k=1}^{\infty} \left( 1 - \dfrac{x^2}{k^2\pi^2} \right)$ | ||
Revision as of 07:32, 27 July 2014
The sine function, usually written $\sin$, is the solution of the second order initial value problem $y=-y;y(0)=0$.
Properties
Proposition: $\sin(x)=\displaystyle\sum_{k=0}^{\infty} \dfrac{(-1)^kx^{2k+1}}{(2k+1)!}$
Proof: proof goes here █
Proposition: $\sin(x) = x \displaystyle\prod_{k=1}^{\infty} \left( 1 - \dfrac{x^2}{k^2\pi^2} \right)$
Proof: proof goes here █
