SOLUTION: Find all solutions in the interval [0,2PI] to the equation {{{cos^(2)(x=1)}}}. a. x = 0, PI/2 b. x = 0, PI c. x = PI/2 3PI/2 d. x = 0, PI/2, PI, PI/2

Algebra ->  Algebra  -> Trigonometry-basics -> SOLUTION: Find all solutions in the interval [0,2PI] to the equation {{{cos^(2)(x=1)}}}. a. x = 0, PI/2 b. x = 0, PI c. x = PI/2 3PI/2 d. x = 0, PI/2, PI, PI/2      Log On

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Question 73943This question is from textbook Algebra and Trigonomerty
: Find all solutions in the interval [0,2PI] to the equation cos%5E%282%29%28x=1%29.
a. x = 0, PI/2
b. x = 0, PI
c. x = PI/2 3PI/2
d. x = 0, PI/2, PI, PI/2This question is from textbook Algebra and Trigonomerty

Found 2 solutions by jim_thompson5910, ffc_01:
Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!

Take the square root of both sides
Take the arc cosine of both sides (this undoes the cosine)

And
If we let n=0 we get x= and if we let n=1 we get x= which is in the interval

So in the interval , the solutions are: x=0 and x=, and x=. However, notice how there isn't a x= answer. I would double-check your book to see if you copied the question right. Besides the missing solution, the answer appears to be b) since 0 and are in it. Hope this makes sense.

Answer by ffc_01(9) About Me  (Show Source):
You can put this solution on YOUR website!
I think the question was supposed to be cos%282x%29=1
In which case...
The interval is
0 < 2x < 2PI these can also be equal
0 < x < PI
and
cos(2x)= 1
2x = 0 and 2PI
x = 0 and PI