Sine function

Overview


The sine function expresses the relationship between lengths of right triangle. Specifically, the sine of an angle {% \theta %} is the ratio of the length of the opposite side of the triangle divided by the length of the hypotenuse.

Relationship to Circle


A particularly instructive way to understand the sine is to plot a circle with radius 1. A point is chosen on the circle, where the very far right point is assigned a {% \theta=0 %}. Then the sine is equal to the projection of the selected point on the y-axis.

Relevant Formulas


  • {% sin(a + b) = sin (a) cos (b) + cos (a) sin (b) %}
  • {% \displaystyle \frac{d \; sin(x)}{dx} = cos(x) %}