SOLUTION: Help very much thanked! Find the exact solution: tan^(2)theta + sqrt(3)tantheta=0 on [0,2pi).

Algebra ->  Trigonometry-basics -> SOLUTION: Help very much thanked! Find the exact solution: tan^(2)theta + sqrt(3)tantheta=0 on [0,2pi).      Log On


   

Question 1154882: Help very much thanked!
Find the exact solution:
tan^(2)theta + sqrt(3)tantheta=0 on [0,2pi).
Found 2 solutions by ewatrrr, ikleyn:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi  

Find the exact solution on [0,2pi): 

tan%5E2%28theta%29+%2B+sqrt%283%29tan%28theta%29=0

%28tan%28theta%29%29%28tan%28theta%29+%2B+sqrt%283%29%29=0

Agree:

tan%28theta%29=+0

+green%28theta+=+0%29 0r +green%28theta+=+pi%29



tan%28theta%29+%2B+sqrt%283%29+=+0

tan%28theta%29+=+-sqrt%283%29

green%28theta+=+%282%2F3%29pi%29+ 0r green%28theta+=+%285%2F3%29pi%29+

Answer by ikleyn(52890) About Me  (Show Source):
You can put this solution on YOUR website!
.

tan%5E2%28x%29 + sqrt%283%29%2Atan%28x%29 = 0   ===========>


tan%28x%29%2A%28tan%28x%29+%2B+sqrt%283%29%29 = 0.



EITHER  tan(x) = 0  OR  tan(x) + sqrt%283%29 = 0.



If tan(x) = 0, then there are TWO solutions  x = 0  and  x = pi  in the given interval.



If tan(x) + sqrt%283%29 = 0,  then  tan(x) = -sqrt%283%29  and there are TWO solutions  x = 2pi%2F3  and  x = 5pi%2F3.



In all, the given equation has  4 (four, FOUR)  solutions in the given interval.

Solved.