How does this work? I'm very confused about the phi is solved using inverse sin. knowing: A=(c[itex]^{2}_{1}[/itex]+c[itex]^{2}_{2}[/itex])[itex]^{1/2}[/itex] and c[itex]_{2}[/itex]= Acos([itex]\phi[/itex]) solve for [itex]\phi[/itex] which yields: [itex]\phi[/itex]=sin[itex]^{-1}[/itex][itex]\frac{c_{2}}{(c^{2}_{1}+c^{2}_{2})^{1/2}}[/itex]=tan[itex]^{-1}[/itex][itex]\frac{c_{2}}{c_{1}}[/itex] I'm not sure how we use the inverse sin to find the phi in the cos function. I thought to get the inside of the parenthesis of cos you would use inverse cos, or cos[itex]^{-1}[/itex]. Where am I going wrong?
Your math expressions are yielding an error here. Just as there are many trigonometric relationships, so there are apparently just as many relations between their inverses. See http://en.wikipedia.org/wiki/Inverse_trigonometric_functions As always, start with the easiest, defining relationships and build out from there. Note that as sine and cosine are related by complementary angles, so are their inverses.
I thought this was an error, but the solutions manual to my quantum mechanics class AND the handwritten solutions provided by my professor both have this error. Thank you for confirming!!