Question

so for problems like arctan(-1)...
do we only find the value that is avaiable until pi since the range for arctan is pi/2???

Answer 1

Not sure what you mean... There is only one value of \(\arctan(-1)\), which depends on the definition of \(\arctan\). The standard definition is to take the branch of \(\tan x\) that passes through the origin (and hence has restricting the domain to \(-\dfrac{\pi}{2}<x<\dfrac{\pi}{2}\)) and invert that.