Definition:Cosine/Real Function
< Definition:Cosine(Redirected from Definition:Real Cosine Function)
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Definition
The real function $\cos: \R \to \R$ is defined as:
| \(\ds \cos x\) | \(=\) | \(\ds \sum_{n \mathop = 0}^\infty \paren {-1}^n \frac {x^{2 n} } {\paren {2 n!} }\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 1 - \frac {x^2} {2!} + \frac {x^4} {4!} - \frac {x^6} {6!} + \cdots + \paren {-1}^n \frac {x^{2 n} } {\paren {2 n}!} + \cdots\) |
Also see
Sources
- 1960: Walter Ledermann: Complex Numbers ... (previous) ... (next): $\S 2$. Geometrical Representations
- 1969: J.C. Anderson, D.M. Hum, B.G. Neal and J.H. Whitelaw: Data and Formulae for Engineering Students (2nd ed.) ... (previous) ... (next): $4.$ Mathematics: $4.2$ Series
- 1977: K.G. Binmore: Mathematical Analysis: A Straightforward Approach ... (previous) ... (next): $\S 16.2$