How do you solve #sin 3x = 0#?

4 Answers
Nghi N.
May 8, 2015

sin 3x = 0
#a. sin 3x = 0 = sin 0 -> x = 0#
#b. sin 3x = 0 = sin pi -> 3x = pi -> x = pi/3#
#c. sin 3x = 0 = sin 2pi -> 3x = 2pi-> x = (2pi)/3#

Nghi N.
Oct 20, 2015

Solve sin 3x = 0.

Explanation:

There is another way to solve sin 3x = 0.
Use the trig identity: #sin 3x = 3sin x - 4sin^3 x#
#sin 3x = sin x(3 - 4sin^2 x)#

a. sin x = 0 --> x = 0, and #x = pi#, and #x = 2pi.#
b. #(3 - 4sin^2 x) = 0#
#4sin^2 x = 3#
#sin^2 x = 3/4# --> #sin x = +- sqrt3/2#
- When #sin x = sqrt3/2# --> #x = pi/3# and #x = 2pi/3#
- When #sin x = -sqrt3/2# --> #x = - pi/3# and #x = -2pi/3.#

José F.
Mar 16, 2016

#sin 3x=0#

#sin 3x=sin kpi, k in ZZ#

#3x= kpi, k in ZZ#

#x= (kpi)/3, k in ZZ#

Jacobi J.
Feb 22, 2018

#x=0#

Explanation:

We start by taking the inverse sine (#arcsin#) of both sides. Arcsin cancels with #sin# and we get:

#3x=arcsin(0)#

#3x=0#

#x=0#

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