Objectives: In this tutorial, we derive the formula for finding the slope of a tangent line to a curve defined by an equation in polar coordinates. A couple of examples are worked to illustrate the use of this formula. After working through these materials, the student should be able

• to find symbolically the slope of the tangent line to the graph of a polar curve.

Theorem. Suppose that r = f(q) is a polar curve. The slope of the tangent line is given by

• Discussion [using Flash]

• Examples.

  • Find slope of tangent line to r(q) = 2 + 3 cos(8q) at q = 3 p/4.
    Discussion [using Flash]

  • Find slope of tangent line to r = sin(5q) at q = p/3.
    Discussion [Using LiveMath]