SOLUTION: Give a general solution in radians using the unit circle 3 tan of x minus the square root of three equals zero 3 tan of x equals the square root of three tan of x equals square

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Question 787558: Give a general solution in radians using the unit circle
3 tan of x minus the square root of three equals zero
3 tan of x equals the square root of three
tan of x equals square root of 3 over 3
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
3tan%28x%29-sqrt%283%29=0
3tan%28x%29=sqrt%283%29
tan%28x%29=sqrt%283%29%2F3

We know that tan%28pi%2F6%29=sqrt%283%29%2F3 (or tan%2830%5Eo%29=sqrt%283%29%2F3 if using degrees). For that angle sin%28pi%2F6%29=1%2F2 and cos%28pi%2F6%29=sqrt%283%29%2F2
That is the only solution for -pi%2F2%3Cx%3Cpi%2F2 (or -90%5Eo%3Cx%3C90%5Eo if using degrees).
The function does not exist for x=-pi%2F2 or x=pi%2F2, where cos%28x%29=0.
In between those values tan%28x%29 increases continuously.

We also know that if tan%28x%29 exists, tan%28x%2Bpi%29=tan%28x%29, so the funcion's values repeat at pi intervals, and we say that the function has period pi.
So there are infinite solutions that can be all expressed as
highlight%28x=pi%2F6%2Bk%2Api%29 for all k integers (or highlight%28x=30%5Eo%2Bk%2A180%5Eo%29 for all k integers if you measure angles in degrees).