arc/notes
1
0
Fork 0
Code Issues Pull Requests Actions Packages Projects Releases Wiki Activity

vault backup: 2024-09-18 12:12:12

Browse Source
This commit is contained in:
zleyyij 2024-09-18 12:12:12 -06:00
parent 867c6b849f
commit 6e475df77a
1 changed files with 14 additions and 6 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

16
education/math/MATH1060 (trig)/Identities.md
View File

@ -6,14 +6,22 @@ $$ tan \theta = \frac{y}{x} $$
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 $1/v$. 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 $1/v$.
| Base Identity | Inverse Identity | Alternate Identities | Alternate Inverse Identities | | Base Identity | Inverse Identity | Alternate Identities | Alternate Inverse Identities |
| ----------------------------- | ------------------------------ | --------------------------------------------- | ------------------------------------------------------------------------- | | ----------------------------- | ------------------------------ | --------------------------------------------- | --------------------------------------------------------------------- |
| $$ sin\theta = y $$ | $$ csc\theta = \frac{1}{y} $$ | | $$ csc\theta = \frac{1}{sin\theta} $$ | | $$ sin\theta = y $$ | $$ csc\theta = \frac{1}{y} $$ | | $$ csc\theta = \frac{1}{sin\theta} $$ |
| $$ cos\theta = x $$ | $$ sec \theta = \frac{1}{x} $$ | | | | $$ cos\theta = x $$ | $$ sec \theta = \frac{1}{x} $$ | | $$ sec\theta = \frac{1}{cos\theta} $$ |
| $$ tan\theta = \frac{y}{x} $$ | $$ cot\theta = \frac{x}{y} $$ | $$ tan\theta = \frac{sin\theta}{cos\theta} $$ | <br>$$ cot\theta = \frac{1}{tan\theta} = \frac{cos\theta}{sin{\theta}} $$ | | $$ tan\theta = \frac{y}{x} $$ | $$ cot\theta = \frac{x}{y} $$ | $$ tan\theta = \frac{sin\theta}{cos\theta} $$ | $$ cot\theta = \frac{1}{tan\theta} = \frac{cos\theta}{sin{\theta}} $$ |
| | | | |
$$ cot \theta = \frac{x}{y} $$ $$ cot \theta = \frac{x}{y} $$
$$ sec\theta = \frac{1}{cos\theta}$$ $$ sec\theta = \frac{1}{cos\theta}$$
$$ csc\theta = \frac{1}{sin\theta}$$ $$ csc\theta = \frac{1}{sin\theta}$$
# Pythagorean Identities # Pythagorean Identities
The Pythagorean identity expresses the Pythagorean theorem in terms of trigonometric functions. It's a basic relation between the sine and cosine functions. The Pythagorean identity expresses the Pythagorean theorem in terms of trigonometric functions. It's a basic relation between the sine and cosine functions.
$$ sin^2 \theta + cos^2 \theta = 1 $$ $$ sin^2 \theta + cos^2 \theta = 1 $$
There are more forms that are useful, but they can be derived from the above formula:
$$ 1 + tan^2\theta = sec^2\theta $$
$$ cot^2 \theta + 1 = csc^2\theta $$
# Even and Odd Identities
- A function is even if $f(-x) = f(x)$.
- A function is odd if $f(-x) = -f(x)$
Cosine and secant are **even*
## Examples