Location of tanget lines involving trig function

[dubb]

Hi,
Here is what the text is saying.
Locations of Tanget Lines
A) For what values of x does g(x) = x - sinx have a horizontal tanget line?

B) For what values of x does g(x) = x - sinx have a slope of 1?


Here's is my work for (A)
g'(x) = 1 - cosx
1-cox=0
-cosx= -1
cosx = 1
horizontal tangent line at 2kpi

For (B)
g'(x) = 1 - cosx
1-cox=1
cosx = 0

tangent line with slope 1 at pi/2 + 2kpi , and 3pi/2 +2kpi

Thanks for your help!

 

[HallsofIvy]

Yes, those are correct.

 

[dubb]

Thanks so much HallsofIvy!!