Answer: x = pi/6 and x = pi/3.
Step-by-step explanation:
We have the function:
y = x + 2*cos(x)
It will have a horizontal tangent at the point where it's derivate is equal to zero.
Then first let's differentiate y.
y' = dy/dx = 1 - 2*sin(x).
Then we must find the value of x between 0 and 2*pi (or 0° and 360°)
y'(x) = 1 - 2*sin(x) = 0.
Let's solve that:
2*sin(x) = 1
sin(x) = 1/2.
We know that:
sin(30°) = 1/2.
and
Sin(120°) = 1/2
Then let's convert 30° into radians.
We know that:
pi = 180°.
Then:
pi/180° = 1.
30° = 30°*(pi/180°) = (30°/180°)*pi = (3/18)*pi = pi/6
120° = (120°/180°)*pi = (12/18)*pi = (1/3)*pi = pi/3.
Then the two values of x are: pi/6 and pi/3.
