# Answer to Question #2256 in Calculus for Waqas Ali

Question #2256

Sketch Cardioid: r = a(1-cosθ)

Please explain me its solution step by step with graph...?

Please tell me as soon as possible...?

Please explain me its solution step by step with graph...?

Please tell me as soon as possible...?

Expert's answer

You can do it in polar coordinates, where θ is the angle and r is the radius.

At θ =0 r = a(1-cos0) =0

θ = 90& r = a(1-cos 90) = a

θ = 180 r = a (1- cos180) = 2a

θ = 270& r = a(1-cos 270) = a

For a= 1:

<img src="http:///" title="" alt=""><img src="../../..//assignments/uploaded_files/static/f8/9c/f89c8c8d728ef2cc1fff06b3a932e3a2.bmp" title="" alt="">

At θ =0 r = a(1-cos0) =0

θ = 90& r = a(1-cos 90) = a

θ = 180 r = a (1- cos180) = 2a

θ = 270& r = a(1-cos 270) = a

For a= 1:

<img src="http:///" title="" alt=""><img src="../../..//assignments/uploaded_files/static/f8/9c/f89c8c8d728ef2cc1fff06b3a932e3a2.bmp" title="" alt="">

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