How to Compute Sine, Cosine & Tangent

Video Transcript

"Hi, I'm Steve Jones, and I'm going to tell you how to compute sines, cosines, and tangents. These are actually ratios based on a right angled triangle. You can see the right angle triangle here, here's the right angle. We label these sides, the opposite side that is the side opposite this angle we call theta. The adjacent side, the one next to this angle, and of course the hypotenuse which is opposite the right angle, in the right angled triangle. So we actually know that when we divide for example the opposite side, the length of the opposite side, by the length of the hypotenuse we get a quantity which we call sin, and we call it sine theta, the sin of the angle theta. There's the opposite divided by the hypotenuse. The Cosine of theta is the adjacent over the hypotenuse. Here's the adjacent side, the length of this side divided by the hypotenuse, the length of the hypotenuse. And finally tan theta, tangent of theta the opposite over the adjacent, the length of this side over the length of this side. Because these numbers, sine, cosine, and tangent for a particular angle are always the same it means that if we know the angle and one of these sides, we can calculate the others in a right angled triangle. This quantity is used in mathematics elsewhere also, but not necessarily in relation to a right angle triangle. Here's a simple example of a ninety degree, forty five degree, forty five degree triangle. A right angled triangle. The length of this side is one, the length of this side is one, and therefore the length of this side is the square root of two. This is Pythagoras Theorem, that this side is the square root of this squared plus this squared. Therefore it's the square root of two. So if I want to do this, sine of forty-five, is the opposite over the hypotenuse, one over root two. Cosine of forty-five is also one over root two, and the tangent of the angle forty-five degrees is one, one divided by one. So sines, cosines, and tangents can be looked up in a table as long as you know the angle then you can work out any side. You know the other angles, but you can work out the length of any of the sines. So that is how to compute with sines, cosines, and tangents."