region enclosed by the cardioid r = 1 - cos(theta)

Question

I need help with solving this please. So confused.

”Find the area A of the region enclosed by the cardioid r = 1 - cos(theta) and the slope m of the tangent line theta = pi/2

Answer 1

You solve this using polar coordinates; see problem 2 at https://ocw.mit.edu/courses/mathematics/18-02sc-multivariable-calculus-fall-2010/3.-double-integrals-and-line-integrals-in-the-plane/part-a-double-integrals/session-50-double-integrals-in-polar-coordinates/MIT18_02SC_pb_36_comb.pdf

This function is 1 - cos(θ) rather than 1 + cos(θ); your answer will be the same, as your cardioid will just flip the cardioid about the y-axis (instead of having (2,0) on the cardioid, you will have (-2, 0)); just follow the same steps.