# Mike's Notes

Assorted notes

November 8th 2018

# Trigonometry

Always helps to remember these.

## Identities

• a - adjacent
• o - opposite
• h - hypotenuse

## $sin^{2}\theta + cos^{2}\theta = 1$

Take a right angle triangle, with sides labelled ‘a’, ‘b’, and ‘c’.

Using the identities, we can then replace $\frac{a}{c}$ with sin, and $\frac{b}{c}$ with cos.

## $a^{2} + b^{2} = c^{2}$

The proof for $a^{2} + b^{2} = c^{2}$ works best for me visually.

There a few different methods to proove the relationship, this page has a nice summary of several.

We use $A$ to represent the area of the larger square. We can calculate A in 2 ways; the area of the large square, or as an addition of the areas of the 4 triangles and the smaller square.

tags: math - trigonometry - linearalgebra