SOLUTION: I'm having trouble understanding how this problem works, I get that when you take the square away from the cos the 1/2 becomes 1/4. but how does 1/4 equate to π/4? find all

Algebra ->  Trigonometry-basics -> SOLUTION: I'm having trouble understanding how this problem works, I get that when you take the square away from the cos the 1/2 becomes 1/4. but how does 1/4 equate to π/4? find all      Log On


   

Question 986762: I'm having trouble understanding how this problem works, I get that when you take the square away from the cos the 1/2 becomes 1/4. but how does 1/4 equate to π/4?
find all of the exact solutions of the equation and then list those solutions which are in the interval [0, 2π)
cos^2(x)=1/2
Found 2 solutions by josgarithmetic, solver91311:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%28cos%5E2%28x%29%29=cos%28x%29=0%2B-+sqrt%281%2F2%29

cos%28x%29=0%2B-+1%2Fsqrt%282%29, and then rationalize the denominator.

Look on the unit circle. For the interval you want, for n=1,2,3,4,5,6,7
highlight%28x=n%28pi%2F4%29%29.


-
pi%2F4 is one of the common reference angles, for cos%28x%29=pi%2F4.

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


How did you get to when taking the square root of ? . .






The -coordinate of the intersection of the terminal ray of an angle at the origin and the unit circle is the cosine of the angle. So look at the unit circle and find all of the angles where the point on the circle has an -coordinate of either or .

Your given interval is [0,2π), so you need to find all four places with this value of -coordinate.



John

My calculator said it, I believe it, that settles it