SOLUTION: I would like some help regarding the following: Find all values of x in [0,360) in degrees, given that: {{{ cot(x/3)= sqrt( 3 ) }}} I know that cot is the same as {{{ arctan (1/x

Algebra ->  Trigonometry-basics -> SOLUTION: I would like some help regarding the following: Find all values of x in [0,360) in degrees, given that: {{{ cot(x/3)= sqrt( 3 ) }}} I know that cot is the same as {{{ arctan (1/x      Log On


   

Question 833905: I would like some help regarding the following:
Find all values of x in [0,360) in degrees, given that: +cot%28x%2F3%29=+sqrt%28+3+%29+
I know that cot is the same as +arctan+%281%2Fx%29+, and have figured out that +arctan%28+1%2Fsqrt%28+3+%29%29+ is equal to 30 degrees, but I need help in figuring out how to determine the rest of the values, as well as the answers.
Thanks in advance.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
You probably meant that cot%28theta%29=1%2Ftan%28theta%29 <--> tan%28theta%29=1%2Fcot%28theta%29,
so applying that to your problem,
+cot%28x%2F3%29=+sqrt%28+3+%29+ --> tan%28x%2F3%29=+1%2Fsqrt%28+3+%29+.
It is true that tan%2830%5Eo%29=1%2Fsqrt%283%29 and that arctan%281%2Fsqrt%283%29%29=30%5Eo .
It is also true that tan%2830%5Eo%2B180%5Eo%29=tan%28210%5Eo%29=1%2Fsqrt%283%29 ,
and that, generalizing, tan%2830%5Eo%2Bn%2A180%5Eo%29=1%2Fsqrt%283%29 for any integer n .
x%2F3=30%5Eo means x=3%2A30%5Eo so highlight%28x=90%5Eo%29 is a solution,
and it is the only one with x in [0,360) in degrees.
The other possible angle values do not lead to solutions with x in [0,360):
x%2F3%3E=210%5Eo --> x%3E=3%2A210%5Eo --> x%3E=630%5Eo , and
x%3C=30%5Eo-180%5Eo --> x%3C=-150%5Eo --> x%3C=3%2A%28-150%5Eo%29 --> x%3C=-450%5Eo