Tanx=(-2sqrt3/3)sinx 0<x<2pi What are all possible solutions?

2 Answers
Nghi N.
Oct 23, 2015

Solve #tan x = ((-2sqrt3)/3)sin x#

Ans: #0, pi, 2pi, (+- 5pi)/6#

Explanation:

#sin x/(cos x) = ((-2sqrt3)/3)sin x#
#sin x + ((2sqrt3)/3)sin x.cos x = 0#

#sin x(1 + ((2sqrt3)/3)cos x) = 0#
a. sin x = 0 --> x = 0; #x = pi#; and #x = 2pi#
b.# (2sqrt3/3)cos x = -1# --> #cos x = -3/(2sqrt3) = - sqrt3/2# -->
#x = +- 5pi/6#.

Kat
Oct 24, 2015

The correct answer { #0,(5pi)/6,pi,(7pi)/6#}

Explanation:

I don't know why.

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