Real Trigonometric Functions are Continuous

Theorem

The trigonometric functions on the real numbers $\R$:

sine

cosine

tangent

cotangent

secant

cosecant

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)