SOLUTION: Find all solutions to 2cos(0)=1 on the interval 0≤0<2π 0= Give your answers as exact values, as a list separated by commas detailed help please.

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Question 1183230: Find all solutions to 2cos(0)=1 on the interval 0≤0<2π
0=
Give your answers as exact values, as a list separated by commas
detailed help please.

Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
let x = theta.
your equation becomes:
2 * cos(x) = 1 on the interval 0 <= x < 2pi radians
since 2 * pi radians = 360 degees, then:
2 * cos(x) = 1 on the interval 0 <= x < 360 degrees.
divide both sides of that equation by 2 to get:
cos(x) = 1/2 on the interval 0 <= x <= 360 degrees.
cos(x) = 1/2 when the angle = 60 degrees.
this is the same as:
arccos(1/2) = 60 degrees.
that would be the reference angle.
cosine is positive in the first and fourth quadrant.
the equivalent angle in the fourth quadrant is equal to 360 - 60 = 300 degrees.
since cosine is negative in the second and third quadrant, the angle is a solutionj only in the first and fourth quadrant.
your solution is then x = 60 or 300 degrees when 0 <= x < 360 degrees.
60 degrees * pi / 180 = pi/3 radians.
300 degrees * pi / 180 = 5pi/3 radians.
your solution, in radians, is x = pi/3 or 5pi/3 when 0 <=x < 2pi,
on a graph, this looks like this:

first quadrant goes from 0 to pi/2.
second quadrant goes from pi/2 to pi.
third quadrant goes from pi to 3pi/2.
fourth quadrant goes from 3pi/2 to 2pi.