Question

In the interval 0 degrees < x < 360 degrees, find the values of x for which cos x = -0.4226. Give your answers to the nearest degree.

Answer 1

115° and 245°

Explanation:

Given

cos x = - 0.4226

Since cos x < 0 then x is an angle in the second / third quadrants, thus

x =
`cos^(-1)` (0.4226) = 65° ← related acute angle , thus

x = 180° - 65° = 115° ← angle in second quadrant

x = 180° + 65° = 245° ← angle in third quadrant