Help finding the angle of a curve where it touches the x-axis

[fholm11]

Hi, I understand most of this question, but what i do not understand is where the 2pi comes from. I think it has something to do with exact angles.

 

[Dr.Peterson]

Hi, I understand most of this question, but what i do not understand is where the 2pi comes from. I think it has something to do with exact angles.

The inverse cosine gives one intersection, namely the first (which is in quadrant II). They subtract this from [MATH]2\pi[/MATH] to get the second intersection, in the second half-cycle (quadrant III). This could also have been done in terms of reference angles.