Sine and Cosine are Cofunctions
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Theorem
The sine and cosine are cofunctions:
\(\ds \forall x \in \R: \, \) | \(\ds \sin x\) | \(=\) | \(\ds \map \cos {90 \degrees - x}\) | |||||||||||
\(\ds \cos x\) | \(=\) | \(\ds \map \sin {90 \degrees - x}\) |
Proof
We have:
Hence the result by definition of cofunction.
$\blacksquare$
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): cofunctions
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): cofunctions