If COS theta = 2/3 what are all the possible angles

Question

I need to know all the possible angles if cos theta = 2/3  

Answer 1

The cos is positive in QI and QIV

cos^-1 0.6666 = 0.841 radians, or 5.436 radians

 

Therefore all angles are o.841 + 2k radians, and 5.436 + 2k radians

 

Answer 2

Use your graphing calculator to see the periodicity.

arccos(2/3) = .84

cos ±.84 = 2/3 and .84 ± 2kπ where k is an integer