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 6m from the front of the stage and the boundary of the optimal pickup region is given by the given cardioid r=12+12sin(theta), where r is measured in meters and the microphone is at the pole. The musicians want to know the area they will have on the stage within the optimal pick up range of the microphone.

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