Posted by **shan** on Wednesday, April 16, 2008 at 9:09am.

solve 0=(3^0.5)tan(x+(pi/6))+1 and find all general solutions

- math -
**Reiny**, Wednesday, April 16, 2008 at 12:47pm
(3^0.5)tan(x+(pi/6))+1 = 0

I am going to let x=pi/6 = y for easier typing

(3^0.5)tan(y)+1 = 0

tany = -1/√3 ...... ah!, tan 30º = +1/√3

so y must be in the second or fourth quadrants.

y = 150º or y = 330º or (5pi/6, 11pi/6)

then x+pi/6 = 5pi/6

x = 2pi/3

or

x+pi/6 = 11pi/6

x = 5pi/3

the period of your function is pi

so the general solutions:

x = 2pi/3 + kpi or

x = 5pi/3 + kpi , where k is an integer.

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