Real Trigonometric Functions are Continuous
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Theorem
The trigonometric functions on the real numbers $\R$:
are all continuous at every point of their domain.
Proof
In turn:
- Real Sine Function is Continuous
- Real Cosine Function is Continuous
- Real Tangent Function is Continuous
- Real Cotangent Function is Continuous
- Real Secant Function is Continuous
- Real Cosecant Function is Continuous
$\blacksquare$
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): continuous function (continuous mapping)
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): continuous function (continuous mapping, continuous map)