Why not? 1/3 is between -1 and 1, of course, there is a reference angle. Any calculator will tell you that cos(70.53)= 1/3 (approximately). The problem did say "use exact solutionswhenever possible.

Or, if you prefer,exactsolutions would be and .

2cos(x) + 1 = 0

2cos(x) = -1

cos(x) = -1/2

Quadrants II and III

Reference Angle= 60 degrees

180 - 60 = 120 degrees

180 + 60 = 240 degrees

Therefore, so far, I have solved for the values: 120 degrees and 240 degrees