Sines and Cosines

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Sines and Cosines

I found this diagram useful when I was learning about trigonometry. It demonstrates the relationship between an angle and its sine and cosine, and helps to develop an understanding of the values of sine and cosine for different sizes of angle.

Imagine an angle drawn from the centre of a circle of radius 1. The line will always have a length of 1. If you project a line downwards from the end of the line to the horizontal axis, the point where the line meets the axis is the cosine of the angle. A line projected across to the vertical 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.

The diagram doesn't show the tangent, because there isn't enough room. If you imagine a vertical tangent to the right of the circle, the value of the tangent of the angle is where the line from the centre of the circle would meet that line if it projected beyond the circumference of the circle.

If you would like to know more about writing computer programs to draw circles circles, look at the circles page.

NB. There is a bug in the Android Browser (sometimes known as "Internet") which means that the canvas isn't cleared properly when the line is moved - try using Chrome instead if you have this problem.