Answer:
See attached graph for the two functions
y = cos(x)
y = 0.5
Solution set for cos(x) i.e. the values of x for which cos(x) = 0.5 in the interval 0 < x < 2π are
{π/3, 5π/3)
or
{1.05, 5.24} in decimal
Explanation:
I moved the original horizontal up to y = 0.5
The solutions to the two equations are where the two functions intersect
There are two intersection in the interval 0 ≤ x ≤ 2π and are at the points labeled A and B
The two points can be obtained by setting
cos(x) = 0.5 and solving for x
cos(x) = 0.5
=> x = cos⁻¹ (0.5)
= 60° and 300° in the range 0 ≤ x ≤ 2π where 2π = 360°
In terms of π,
Since π radians = 180°, 1° = π/180 radians
60° = π/180 x 60 = π/3 radians
300° = π/180 x 300 = 5π/3 radians
Therefore the solutions to cos(x) = 0.5 are
x = π/3 and x = 5π/3
The solution set is written as {π/3, 5π/3}
In decimal
π/3 = 1.04719 ≈ 1.05
5π/3 = 5.23598 ≈ 5.24
Solution set in decimal: {1.05, 5.24}