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 5 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, 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. (Give your answer correct to two decimal places.)
r = 10 + 10sin(θ)

Question

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 5 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, 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. (Give your answer correct to two decimal places.)
r = 10 + 10sin(θ)

anonymous · Answer

Please help

anonymous · Answer

attachment

anonymous · Answer

I do not understand the steps on webassign

tkhunny · Answer

You need boundaries.  You are told the angle to start.  There is another one on the left to stop.

You need to know how to find an area in polar coordinates.

It's all there.  Where do you stop following the demonstration?

anonymous · Answer

Ok i was lost right where it starts to integrate

tkhunny · Answer

Starting is $\alpha$.  In the demonstration, they recognized the symmetry and stopped at $\pi/2$.  Notice the odd "2" out in front.  This is the direct result of the symmetry.

anonymous · Answer

Thank u for the tip tkhunny!