# Polar Calculus

This triangle is important for solving many problems related to polar coordinates.

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.