Sines and Cosines

This diagram demonstrates the relationship between an angle and its sine and cosine and helps you understand the values of sine and cosine for different angles.

Imagine an angle drawn from the centre of a circle of radius 1 - it always have a length of 1. If you project downwards from the end of the line, the point where the line meets the x-axis is the cosine of the angle. Projecting across to the y-axis will give the sine. As the length of the line is always 1, you can use Pythagoras to show that the sum of the squares of the sine and cosine is 1.

Tangents aren't shown. Imagine a vertical tangent to the right of the circle - the value of the tangent is where the line from the centre of the circle would meet the tangent if it projected beyond the circumference of the circle.

You can read about using trigonometry to draw circles on the circles page.