# An Introduction to Trigonometry

## What are Sin, Cos and Tan?

Sine, Cosine and Tangent are functions, sitting them in the same family as familiar things such as product and sum. Their abbreviations are Sin, Cos and Tan respectively. Each one lends itself to a different periodic graph:

$$\sin$$

$$\cos$$

$$\tan$$

## Simple examples

Trig functions are used on angles, so we must know whether we're using degrees or radians! So how are these functions used? Here's a few examples using degrees;

$$\sin(30)=\frac{1}{2}$$

$$\cos(-74)\simeq0.275637$$

With radians used in exactly the same way but the horizontal axis has a different scale;

$$\tan\left(\frac{\pi}{4}\right)=1$$

This is all explained in more depth on the graphs page

## Exponents: notation

We know that $$(x+1)\times(x+1)=(x+1)^2$$ but it's not so obvious where to put the exponent (in this case 2) when we have $\sin(x)\times\sin(x)$ You'll rarely see it written $\sin(x)\times\sin(x)=\sin(x)^2\hspace{12 pt}$ It is instead usually written as $\sin(x)\times\sin(x)=\sin^2(x)\hspace{12 pt}$ This avoids confusion over what the exponent relates to.