Find all angles between 0 and 2 pi satisfying the condition

Find all angles between 0 and 2 pi satisfying the condition cos x = 1/2. Separate your answers with commas.

Solution

Given

cos x = 1/2

x = cos^-1(1/2)

The cosine trigonometric function is positive in two quadrants

first quadrant and fourth quadrant

Hence the value of x has two values one in first and second in fourth quadrant

First angle:

x = pi/3

and second one:

x = 2*pi - pi/3

= 5*pi/3

So when the function is solved we get values of x as

x = pi/3, 5*pi/3