SOLUTION: Use inverse functions where needed to find all solutions of the equation in the interval [0, 2π). (Enter your answers as a comma-separated list.) tan^2x+tanx−30=0

Algebra ->  Trigonometry-basics -> SOLUTION: Use inverse functions where needed to find all solutions of the equation in the interval [0, 2π). (Enter your answers as a comma-separated list.) tan^2x+tanx−30=0      Log On


   

Question 1114645: Use inverse functions where needed to find all solutions of the equation in the interval [0, 2π). (Enter your answers as a comma-separated list.)
tan^2x+tanx−30=0
Answer by ikleyn(52797) About Me  (Show Source):
You can put this solution on YOUR website!
.
It is a quadratic equation relative tan(x).


To solve it,  factor the left side


(tan(x)-5)*(tan(x)+6) = 0.


The solutions in the given interval are 


    x = atan(5),        x = atan(5) + pi,


    x = -atan(6) + pi,  x = -atan(6) + 2*pi.


(four solutions, in all).