Opposites Theorem
Jump to navigation
Jump to search
Theorem
| \(\ds \sin \left({- \theta}\right)\) | \(=\) | \(\ds - \sin \theta\) | ||||||||||||
| \(\ds \cos \left({- \theta}\right)\) | \(=\) | \(\ds \cos \theta\) | ||||||||||||
| \(\ds \tan \left({- \theta}\right)\) | \(=\) | \(\ds - \tan \theta\) |
Proof
| \(\ds \sin \left({- \theta}\right)\) | \(=\) | \(\ds - \sin \theta\) | Sine Function is Odd | |||||||||||
| \(\ds \cos \left({- \theta}\right)\) | \(=\) | \(\ds \cos \theta\) | Cosine Function is Even | |||||||||||
| \(\ds \tan \left({- \theta}\right)\) | \(=\) | \(\ds - \tan \theta\) | Tangent Function is Odd |
$\blacksquare$
Comment
The concept of bagging up these identities into one, and calling it the Opposites Theorem, seems to be a modern innovation designed to ease the learning of trigonometry in schools.