1.3 KiB
1.3 KiB
Given the formula \sin(\alpha + \beta):
\sin(\alpha + \beta) = \sin(\alpha)\cos(\beta) + \cos(\alpha)\sin(\beta) \sin(\alpha - \beta) = \sin(\alpha)\cos(\beta) - \cos(\alpha)\sin(\beta) Given the formula \cos(\alpha + \beta):
\cos(\alpha + \beta) = \cos(\alpha)\cos(\beta) - \sin(\alpha)\sin(\beta) \cos(\alpha - \beta) = \cos(\alpha)\cos(\beta) + \sin(\alpha)\sin(\beta) Given the formula \tan(\alpha + \beta):
\tan(\alpha + \beta) = \dfrac{\tan\alpha + \tan\beta}{1 - \tan\alpha\tan\beta} \tan(\alpha - \beta) = \dfrac{\tan\alpha - \tan\beta}{1 + \tan\alpha\tan\beta} Cofunctions
Given that cofunctions are two functions that add up to 90 degrees, you can use the trig identities for sum and difference to find cofunctions.
For a right triangle where \alpha = \theta, \beta = \frac{\pi}{2} - \theta.
This means that \sin(\theta) = \cos(\frac{\pi}{2} - \theta)
Using this information, you can derive various cofunction identities.
\sin\theta = \cos(\frac{\pi}{2} - \theta) |
\cos\theta = \sin(\frac{\pi}{2} - \theta) |
|---|---|
\tan\theta = \cot(\frac{\pi}{2} - \theta) |
\cot\theta = \tan(\frac{\pi}{2} - \theta)) |
\sec\theta = \csc(\frac{\pi}{2} - \theta) |
\csc\theta = \sec(\frac{\pi}{2} - \theta) |