The Definition of Cosine and Sine

In this post I'd just like to briefly give the definition of cosine and sine, and also show a simple property involving both of them.



Consider a right triangle containing an angle θ. All such triangles are just scalar multiples of each other. Therefore the ratio of the adjacent side to the hypotenuse is a fixed value.



We'll call this ratio the cosine of θ. Similarly, we can define the sine of θ as the ratio of the opposite side to the hypotenuse

Now, we can show that



First we'll substitute



And by the Pythagorean Theorem



And so