SOLUTION: Can you please help me with the following problem, the following equation involves multiple angles. solve the equation on the interval [0,2pi) tan x/2=-sqrt 3/3 Work I have done:

Algebra ->  Trigonometry-basics -> SOLUTION: Can you please help me with the following problem, the following equation involves multiple angles. solve the equation on the interval [0,2pi) tan x/2=-sqrt 3/3 Work I have done:      Log On


   



Question 1012326: Can you please help me with the following problem,
the following equation involves multiple angles. solve the equation on the interval [0,2pi) tan x/2=-sqrt 3/3
Work I have done:
tan=-sqrt 3/3 = 5pi/6,11pi/6
x/2=5pi/6+2kpi, x/2=11pi/6+2kpi

Answer by ikleyn(52906) About Me  (Show Source):
You can put this solution on YOUR website!
.
solve the equation on the interval [0,2pi): tan x/2=-sqrt 3/3
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tan%28x%2F2%29 = -sqrt%283%29%2F3  ----->

x%2F2 = %285pi%29%2F6 or/and x%2F2 = %2811pi%29%2F6.


If x%2F2 = %285%2Api%29%2F6, then x = 5pi%2F3. It is one solution.


If x%2F2 = %2811%2Api%29%2F6, then x = 11pi%2F3. It is greater than 2pi, and you need to reduce it to the reference angle, which is 5pi%2F3.

Thus the problem has a unique solution x = 5pi%2F3.