Where does the sine function come from?
- Richard Bitgood
Below is a unit circle. First drag the point to see the relationship between the angle, the sides of the triangle, the unit circle and the sine ratio. Then click the checkbox to turn on tracing and see how this relates to graphing the function f(x)=sin(x).
Notice that the angle theta and the x-value of the point on f(x)=sin(x) are the same. Why are the y-value's the same for the point on the unit circle and the point on f(x)=sin(x)? What would the sine function do if x gets larger than one revolution (x>2*pi)? Think about why we didn't use f(x)=cos(x) to show this.