A Proper Go At Explaining Trig

Alright, well, clearly it is the study of angles and triangles and by use of the unit circle, of circles too.

We talk about sin, cosine, and tan a lot in the basic stuff.

Although we learned SohCahToa at school, it really only applies to right angled triangles. But by using the unit circle (radius 1, centre at the origin) and drawing a right angled triangle inside it, we can calculate basic values of sine, cosine and tan, which hold for any angle and can be used in calculations involving any triangle.

The sine of an angle is a measurement of its distance from the horizontal axis, which can be negative or positive and which can be between 1 and -1 inclusive. If you think of an angle sweeping up around the circle, it reaches its furthest point from the axis (ie sin of 1) at 90 degrees.

The cosine of an angle is a meaurement of the distance from the vertical y axis of a point on the end of the angle; again, between 1 and -1.

The tan of an angle is a measurement of whether a line of angle x would meet a tangent to the circle drawn at right angles to the radius (the x axis) near, far, or not at all. The tan can have any value. Calculators really don't like being asked tan 90 or tan 270 because the lines of these angles will never meet a tangent.

There are some cool diagrams on the wikipedia page that show these things in action.