Just a few notes on how to proceed on the penultimate homework of the semester. We're to show that the solutions for the 30/60/90 triangular waveguide given in the last homework set will also work for a waveguide that's formed from an equilateral traingle. The three corners of the equilateral traingle are located at $\left(x,y\right) = \left(0, 0\right)$, $\left(x,y\right) = \left(a, a/\sqrt{3}\right)$, and $\left(x,y\right) = \left(a, -a/\sqrt{3}\right)$. This falls out immediately from last week's homeowrk. Because the sine function is peiodic in $\pi$ over the domain from $\left(-\infty, \infty\right)$, the solution given last week in terms of sines will still evaluate to zero on the wall that falls at negative $y$. coordites. The positive $x$ coordinates of the functions will evaluate to 0 on the wall in the same manner they did before??? There's an issue here. It's products of the $x$ and $y$ sinusoids that all sum to zero. These will need t...