Timeline for Griffiths Electrodynamics Problem 9.39: How can $\sin(\theta_T)$ be greater than one?

6 events

when toggle format	what		by	license	comment
May 7, 2019 at 10:45	vote	accept	Mason Hargrave
May 7, 2019 at 10:28	comment	added	John Donne		In particular the condition you're looking for is $\cos{u}=0$. This will give you an imaginary cosine and a real sine
May 7, 2019 at 10:16	comment	added	John Donne		You need to divide by $i$ in the sine formula!
May 7, 2019 at 10:03	history	edited	John Donne	CC BY-SA 4.0	Fixed mistakes
May 7, 2019 at 9:59	comment	added	Mason Hargrave		So for imaginary inputs such as $x=iv$ where the real component $u$ is equal to zero and the imaginary component $v>.881$, I can see that $\sin(x) = \frac{e^{ix}-e^{-ix}}{2} >1$ and is real valued. In that exact situation, $\cos(x)$ is also real valued and greater than 1. In order for $\cos(x)$ to be imaginary, $x$ must be pure real. How then am I supposed to interpret that fact that $\sin(\theta_T) > 1$ implies that $\theta_T$ is pure imaginary with $v>.881$ while simultaneously $\cos(\theta_T)$ is imaginary which implies that $\theta_T$ is pure real valued?
May 7, 2019 at 9:28	history	answered	John Donne	CC BY-SA 4.0