MathsLearner
New member
- Joined
- Aug 13, 2017
- Messages
- 27
The problem summary statement is, When recording live a microphone is used with cardioid pickup pattern. suppose the microphone is placed 4m from the front of the stage and the boundary is given by cardioid r = 8 + 8[math] \sin\theta[/math], where r is measured in meters and the microphone at pole. What is the area of the optimal pickup range of the microphone.
My attempt is i am finding the area of the blue region.
The total area is
A = [math]\int_0^{2\pi} \frac {r^2} 2 d\theta[/math]A=[math]\int_0^{2\pi} 32(1+\sin\theta)^2 d\theta[/math] = 301.59
But i am confused how much area i need to subtract. That is which is the point i have to take at [math]0\deg[/math]? What is the angle at which cardioid intersects with the stage. Please advise.
My attempt is i am finding the area of the blue region.
The total area is
A = [math]\int_0^{2\pi} \frac {r^2} 2 d\theta[/math]A=[math]\int_0^{2\pi} 32(1+\sin\theta)^2 d\theta[/math] = 301.59
But i am confused how much area i need to subtract. That is which is the point i have to take at [math]0\deg[/math]? What is the angle at which cardioid intersects with the stage. Please advise.