Question

Calculus Polar help

Answer 1

When recording live performances, sound engineers often use a microphone with a cardioid pickup pattern because it suppresses noise from the audience. Suppose the microphone is placed 4 m from the front on the stage (as in the figure) and the boundary of the optimal pickup region is given by the given cardioid
r = 8 + 8 sin θ,
where r is measured in meters and the microphone is at the pole. The musicians want to know the area they will have on stage within the optimal pickup range of the microphone.