To Teach a Monkey (beta)

Trigonometry

Trig Functions

From this we can infer that $csc$ is the inverse of $sin$ and $sec$ is the inverse of $cos$ . As seen in the data booklet

Pythagorean Identities

This comes from creating a triangle using the unit circle, with the hypotenuse being 1

Inverse Trigonometric Functions

In order to ensure that the Invere trigonometric functions are one to one, there are special range restrictions put on the functions to prevent one input yielding multiple outputs

$arcsin$ and $arctan$ has a domain restriction of $[-\frac{\pi}{2}, \frac{\pi}{2}]$ and $arccos$ has a range of $[0,\pi]$ . This is to ensure that all values -1 to 1 are covered

Compound Angle Identities

As seen in the data booklet

Keep in mind that the sign for the $cos$ identity is the opposite of what if inputted

Trig Graphs

A is the amplitude of the graph

The period is $\frac{2\pi}{b}$ for $sin$ and $cos$ , and $\frac{\pi}{b}$ for $tan$

The vertical shift is $d$

The horizontal shift is $\frac{c}{b}$

Reciprocal Functions

Even and Odd Functions

Inverse Functions

A function has an inverse if and only if it is one-to-one

A functions inverse is by switching the x and y