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education/math/MATH1060 (trig)/Identities.md
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@ -5,11 +5,12 @@ All of the following only apply when the denominator is not equal to zero.
$$ tan \theta = \frac{y}{x} $$
Because the following are inverses of their counterparts, you only need to remember the equivalents for $sin$, $cos$, and $tan$, then just find the inverse by taking $1/v$.
| Identity | Inverse Identity |
| ------------------------------- | ------------------------------ |
| $$ sin\theta = y $$ | $$ csc\theta = \frac{1}{y} $$ |
| $$ cos\theta = x $$ | $$ sec \theta = \frac{1}{x} $$ |
| $$ tan\theta = \frac{sin\theta} | |
| Base Identity | Inverse Identity | Alternate Identities | Alternate Inverse Identities |
| ----------------------------- | ------------------------------ | --------------------------------------------- | ------------------------------------------------------------------------- |
| $$ sin\theta = y $$ | $$ csc\theta = \frac{1}{y} $$ | | $$ csc\theta = \frac{1}{sin\theta} $$ |
| $$ cos\theta = x $$ | $$ sec \theta = \frac{1}{x} $$ | | |
| $$ tan\theta = \frac{y}{x} $$ | $$ cot\theta = \frac{x}{y} $$ | $$ tan\theta = \frac{sin\theta}{cos\theta} $$ | <br>$$ cot\theta = \frac{1}{tan\theta} = \frac{cos\theta}{sin{\theta}} $$ |
| | | | |
$$ cot \theta = \frac{x}{y} $$
$$ sec\theta = \frac{1}{cos\theta}$$
$$ csc\theta = \frac{1}{sin\theta}$$