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:

sine graph


cosine graph


tangent graph


To learn more about the graphs, click here.

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;

tangent graph


tangent graph


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

tangent graph


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.