Solving Equation for M & P - Geometry Explained

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The discussion revolves around solving the equation 5*cos(Wo*t)=M*cos(Wo*t-(pi/6))+5*cos(Wo*t+p) for variables M and P using the phasor method. A geometrical diagram in the z-plane is suggested to visualize the solutions, specifically focusing on the set defined by {z:z=5*exp(j*p)-5 where 0≤p≤2pi}. The user encountered an issue when converting to phasor form, resulting in M=0, which raises questions about its implications. The response indicates that substituting M=0 back into the original equation can help determine the corresponding value of P. This exchange highlights the importance of graphical representation and substitution in solving complex equations in geometry.
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Hi i am trying to solve this problem and i am stuck at finding all possible solutions, can someone please help?

Problem: Solve the following equation for M and P. Obtain all possible answers. Use the phasor method, and provide a geometrica diagram to explain the answers.

5*cos(Wo*t)=M*cos(Wo*t-(pi/6))+5*cos(Wo*t+p)
hint: Describe the figure in the z-plane given by the set {z:z=5*exp(j*p)-5 where 0<(or equal) p <(or equal) 2pi

when i converted to phasor form and solve for M, I got M=0, not sure what that means...
 
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Well, if you insert M=0 in the original equation, you can immediately see what p would be.
 

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