# Trigonometric identities

**Same angles:**

**Opposite angles:**

and

**Supplementary angles:**

and

**Complementary angles:**

and

**Anti-supplementary angles:**

and

**Table**

f(x) | 0° | 30° | 45° | 60° | 90° |
---|---|---|---|---|---|

sin(A) | 0 | 1 | |||

cos(A) | 1 | 0 | |||

tan(A) | 0 | 1 | und | ||

cot(A) | und | 1 | 0 |

**Proof:**

**Angle sum and difference identities**

**Proof:**

Remember that L²=(X2-X1)²+(Y2-Y1)²

The proof relies on the fact that W can be calculated 2 ways:

First way:

Second way:

put them together:

Left side:

Right side:

We can now clearly see that:

or