SOLUTION: i need your help i'm stuck. i have to find the exact solutions when possible for 0 deg<= x <360 deg or approximate the solution cotx=12/13

Algebra ->  Trigonometry-basics -> SOLUTION: i need your help i'm stuck. i have to find the exact solutions when possible for 0 deg<= x <360 deg or approximate the solution cotx=12/13      Log On


   

Question 741077: i need your help i'm stuck.
i have to find the exact solutions when possible for 0 deg<= x <360 deg or approximate the solution
cotx=12/13
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
A calculator can give you an approximate solution.
If cot%28x%29=12%2F13, then tan%28x%29=1%2Fcot%28x%29=13%2F12
and the calculator says that tan%5E%28-1%29%2813%2F12%29=47.29%5Eo so tan%2847.29%5Eo%29=13%2F12
tan%28x%29 is positive and increasing in the first and third quadrant, and has a period of 180%5Eo
The graph below shows y=tan%28x%29 and y=13%2F12
graph%28300%2C300%2C-45%2C405%2C-5%2C5%2Ctan%28pi%2Ax%2F180%29%2C13%2F12%29
So that tan%2847.29%5Eo%29=tan%2847.29%5Eo%2B180%5Eo%29=tan%28227.29%5Eo%29
The only two approximate solutions to cot%28x%29=12%2F13 for 0%3C=x%3C360%5Eo are
highlight%28x=47.29%5Eo%29 and highlight%28x=227.29%5Eo%29