Tanx+sinx, find f', f", intercepts than graph

Just had this on a problem that was due on Tuesday just past, but I have a lingering question about the intercepts.

So this is simple, set it = to zero, simple, but you end up with cosx=-1, this I am struggling with. I know from the f’, and f” about my other critical points, and using a graphing calculator I can see the intercepts are at Pi +KPi where K is an Interger, so how do you map cosx=-1 into this, or am I completely off base here

To complete the picture, my answer tot he problem below

Domain, All Reals except when x is not = to Pi/2 + K*Pi where K is an Interger

First derivative = Sec^2x + cosx

undefined at Pi/2 + K*Pi where K in an Interger

x=0 Pi + K* Pi where K in an Interger

Second Derivative = (2sinx/cos^3)- sinx

Inflection Pi + K * Pi where K is an Interger

No local exptrema