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**MathChick** I have a problem that look like this: cos(3x)=1/ sqrt2

I already got the correct anser but my teacher says i have to give a more detailed description of how i solved it and he says that part of calculatón is wrong, this is my calculation:

The unit circle value for the equation above is 40 degrees or pi/4 radian. after finding this i make 3x=a to make it easier. So i figured that because sin(a)=cos(a) i can from this prove that a=pi/4+2*n*pi ...ooor a=-pi/4+2*n*pi

Then we switch back to 3x and in order to get x alone we need to divide all sides by 3 in both solutions, and that leaves us with the final anwser:

x=pi/12+2*n*pi/3

x=-pi/12+2*n*pi/3

What would you recommend i add or do you see anything incorrect??