calculus-with-polar-coordinates

Finding tangents to polar curves

What is the gradient/tangent of a polar curve?

• Gradients (and tangents) are the same as using Cartesian coordinates

  • i.e. a gradient of 1 in Cartesian coordinates is still a gradient of 1 in polar coordinates

  • a 45° line from “bottom left” to “top right” is a gradient of 1 in both systems

  • the equation of a tangent to a polar curve should be written in polar form

How do I find the tangents to a polar curve?

• Finding the gradient – and so the equation of a tangent – to a polar curve is based on parametric differentiation in Cartesian form

• Since ,  and , it follows that

  • 

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