SOLUTION: Find all values of x that satisfy the equation 2cosx-1=0, in the interval [0, 2pi] The correct answer is one of the following. Which one? A) pi/2, 3pi/2 B) pi/4, 3pi/4

Algebra ->  Equations -> SOLUTION: Find all values of x that satisfy the equation 2cosx-1=0, in the interval [0, 2pi] The correct answer is one of the following. Which one? A) pi/2, 3pi/2 B) pi/4, 3pi/4       Log On


   



Question 1198604: Find all values of x that satisfy the equation 2cosx-1=0, in the interval [0, 2pi]
The correct answer is one of the following.
Which one?
A) pi/2, 3pi/2
B) pi/4, 3pi/4
C) pi/2, 3pi/4
D) pi/6, 5pi/6
E) pi/3, 5pi/3

Found 2 solutions by ikleyn, MathLover1:
Answer by ikleyn(52776) About Me  (Show Source):
You can put this solution on YOUR website!
.

The given equation  2*cos(x) - 1 = 0 is equivalent to 

    2*cos(x) = 1,  or  cos(x) = 1%2F2,


which has the roots  x = pi%2F3  and  x = 5pi%2F3  in the interval [0,2pi) and has no other roots in this interval. 


ANSWER.  Option E).

Solved.

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By the way,  interval  [0,2pi]  is shown  INCORRECTLY  in your post.

The standard and traditional notation for this interval is  [0,2pi)
 with the curved closing parenthesis.


As you write it incorrectly,  I can make my conclusion about your mathematical competency.



Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

2cos%28x%29-1=0, in the interval [0, 2pi]

2cos%28x%29-1=0
2cos%28x%29=1
cos%28x%29=1%2F2
x=cos%5E-1%281%2F2%29
x=pi%2F3


solutions in the interval [0, 2pi]
x=pi%2F3
x+=+%285pi%29%2F3

answer:
E)