FIFINE K658 USB Dynamic Cardioid Microphone with A Live Monitoring, Gain Control, Mute Button

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 of the stage (as in the figure) and the boundary of the optimal pickup region is given by the cardioid r=8 8 sinθ, 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. Answer

in studios and on stages cardioid microphones are often preferred for the richness they add to voices and for their ability to reduce the level of sound from the sides and rear of the microphone sup 2

5.1.5: Special Polar Equations and Graphs