Find all angles θ between 0° and 180° satisfying the given equation cos(θ) = − 2/7

Answer 1

The angle θ is the inverse of the value above such that cos^-1 cos θ = cos^-1 ( -2/7) = cos^-1( -0.2857) , and

θ = 106.6^ο is between 0^ο and 180^ο ,

it is also the set of angles that occurs at the same point every time you add 2π to it

or θ = 106.6^ο + 2πn , where n = 1,2,3,4..., and 2π = 360^ο

θ = ( 106.6^ο + 2π , 106.6^ο + 4π, 106.6^ο + 6π, 106.6^ο + 8π..... ) and so on

Answer 2

cos θ < 0 in QII, 180 ° > θ > 90°

θ = 106.6º