solution to cos problem

Question

find all solutions to cos(angle)=-1/2 in the interval 0≤Angle≤2pi

angle =

Answer 1

cosine is negative in the 2nd and 3rd quadrants

cos60º=1/2 but we want (-1/2)

make a 60º angle with the negative x-axis in the second quadrant leaving a 30º angle with the positive y-axis

90º+30º=120º is one answer

make a 60º angle with the negative x-axis in the third quadrant

180º+60º=240º is the other answer

 

Answer 2

The cos(Θ) is negative in quadrants II & III

 

cos(θ) = -½ means that cos ^-1 (-1/2) = θ = pi ± 60°

 

The two angles satisfying this condition are Θ = 120° and Θ = 240°