What does $\tan x = 1$ mean? I can solve for $x$ by taking the arctangent of both sides but I'm not understanding what the equation means. Does the equation represent the interesection between $y = \tan x$ and $y =1$? Likewise is $\sin x = 2$ said to be undefined as the two curves do not intersect for any real $x$ (they don't cut each other?). I feel that I am missing a key concept in trigonometric equations.
Also to find other solutions of $\tan x = 1$ do I just subtract or add $\pi$ to the principle value?
Thanks

$\tan{x}$ is the ratio of $\sin{x}$ over $\cos{x}$.  Having $\tan{x}=1$ means that $\sin{x}=\cos{x}$.
Now, what angles produce this result?
