Monthly Archives: April 2017

Polar Calculus

This triangle is important for solving many problems related to polar coordinates. Polar Rectangular Triangle showing x, y, r, and theta

From it we get the following important relationships:

`x=r*cos(theta)`

`y=r*sin(theta)`

`r^2=x^2+y^2`

`tan(theta)=y/x`

In polar coordinates we write `r` as a function of `theta`, `r=f(theta)`.

Now consider the equation `x=r*cos(theta)`. If we differentiate with respect to `theta`, the we get `(dx)/(d theta)=(dr)/(d theta)*cos(theta)-r*sin(theta)`.

Similarly, `(dy)/(d theta)=(dr)/(d theta)*sin(theta)+r*cos(theta)`.

These relationships will be useful when looking at slope and arc length, which are concepts from rectangular coordinates.