vault backup: 2024-09-18 12:02:12

education/math/MATH1060 (trig)/Identities.md

@@ -0,0 +1,18 @@
+# Trigonometric Identities
+
+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               |
+| ------------------------------- | ------------------------------ |
+| $$ sin\theta = y $$             | $$ csc\theta = \frac{1}{y} $$  |
+| $$ cos\theta = x $$             | $$ sec \theta = \frac{1}{x} $$ |
+| $$ tan\theta = \frac{sin\theta} |                                |
+$$ cot \theta = \frac{x}{y} $$
+$$ sec\theta = \frac{1}{cos\theta}$$
+$$ csc\theta = \frac{1}{sin\theta}$$
+# Pythagorean Identities
+The Pythagorean identity expresses the Pythagorean theorem in terms of trigonometric functions. It's a basic relation between the sine and cosine functions.
+$$ sin^2 \theta + cos^2 \theta = 1 $$

education/math/MATH1060 (trig)/The Unit Circle.md

@@ -26,19 +26,6 @@ Finding a reference angle:
 | 2        | $180\degree - \theta$ |
 | 3        | $\theta - 180\degree$ |
 | 4        | $360\degree - \theta$ |
-## Other Trigonometric Functions
-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 $1/v$. 
-$$ sec \theta = \frac{1}{x} $$
-$$ csc = \frac{1}{y} $$
-$$ cot \theta = \frac{x}{y} $$
-
-## The Pythagorean Identity
-The Pythagorean identity expresses the Pythagorean theorem in terms of trigonometric functions. It's a basic relation between the sine and cosine functions.
-$$ sin^2 \theta + cos^2 \theta = 1 $$
-
 # Definitions
 
 | Term             | Description                                                                   |