SOLUTION: QUICK! Could someone help me with this question. Solve {{{cos2x=sqrt(2)/2}}} in an algebaic manner and state the general solutions. Best regards in advance...

Algebra ->  Trigonometry-basics -> SOLUTION: QUICK! Could someone help me with this question. Solve {{{cos2x=sqrt(2)/2}}} in an algebaic manner and state the general solutions. Best regards in advance...      Log On


   

Question 61461: QUICK!
Could someone help me with this question.

Solve cos2x=sqrt%282%29%2F2 in an algebaic manner and state the general solutions.

Best regards in advance...
Answer by 303795(602) About Me  (Show Source):
You can put this solution on YOUR website!
cos2x=sqrt%282%29%2F2
Divide top and bottom on the Right Hand Side by sqrt%282%29 to get
cos2x=1%2Fsqrt%282%29%29

Cos (45) = cos (135) =1%2F%28sqrt%282%29%29
So x = 22.5 degrees or x = 67.5 degrees.
The Cos function is periodic so these values will repeat every 360 degrees
so x = 22.5 + 360n where n is any integer
or
so x = 67.5 + 360n where n is any integer