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lgbasallote
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Find all values of x such that \(\sin 2x = \sin x\) and 0 < x < 2\(\pi\)
 one year ago
 one year ago
lgbasallote Group Title
Find all values of x such that \(\sin 2x = \sin x\) and 0 < x < 2\(\pi\)
 one year ago
 one year ago

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lgbasallote Group TitleBest ResponseYou've already chosen the best response.0
i suppose the only way for this to happen is if the x were 0....
 one year ago

JamesWolf Group TitleBest ResponseYou've already chosen the best response.0
yeah or pi, but you specified x < 2pi
 one year ago

lgbasallote Group TitleBest ResponseYou've already chosen the best response.0
hmm i suppose pi works
 one year ago

lgbasallote Group TitleBest ResponseYou've already chosen the best response.0
sin 2x = sin x arcsin both sides 2x = x 2x  x = 0 x = 0 how can i get the other values?
 one year ago

JamesWolf Group TitleBest ResponseYou've already chosen the best response.0
hmmm good question
 one year ago

leedomathgeek Group TitleBest ResponseYou've already chosen the best response.1
sin(2x)=2sin(x)cos(x) Therefore, sin(2x)=sin(x) > 2sin(x)cos(x)=sin(x) 2sin(x)cos(x)sin(x)=0 sin(x)[2cos(x)1]=0 Now either sin(x)=0 > x=0,pi,... or 2cos(x)1=0 > cos(x)=1/2 > x=pi/3
 one year ago

lgbasallote Group TitleBest ResponseYou've already chosen the best response.0
then i suppose the others can be solved by adding pi?
 one year ago

leedomathgeek Group TitleBest ResponseYou've already chosen the best response.1
Why do you want to add a pi?
 one year ago

lgbasallote Group TitleBest ResponseYou've already chosen the best response.0
because one angle is missing
 one year ago

leedomathgeek Group TitleBest ResponseYou've already chosen the best response.1
You have only 3 solutions
 one year ago

leedomathgeek Group TitleBest ResponseYou've already chosen the best response.1
0, pi/3, pi
 one year ago

lgbasallote Group TitleBest ResponseYou've already chosen the best response.0
there's actually 5.. but i know how to get one of the missing angles...
 one year ago

leedomathgeek Group TitleBest ResponseYou've already chosen the best response.1
oh ya i though x between 0 and pi
 one year ago

leedomathgeek Group TitleBest ResponseYou've already chosen the best response.1
sure 2pi is the 4th solution
 one year ago

leedomathgeek Group TitleBest ResponseYou've already chosen the best response.1
and x=2pip/3=5pi/3
 one year ago

leedomathgeek Group TitleBest ResponseYou've already chosen the best response.1
is the 5th solution
 one year ago

lgbasallote Group TitleBest ResponseYou've already chosen the best response.0
oh subtract pi/3 from 2pi...ah yes... the negative angle
 one year ago

leedomathgeek Group TitleBest ResponseYou've already chosen the best response.1
exactly ...since cos(x) is positive in the 4th quad
 one year ago

apple_pi Group TitleBest ResponseYou've already chosen the best response.0
Here's an example you might want to look at: tan(4x) = tan(2x) 0° ≤ x ≤ 360° tan(4x) = tan(2x) ****DONT DO THIS: 4x = 2x INSTEAD... 4x = 180n 2x (Write one side as a general solution) then simplify: 6x = 180n x = 30n then you have all possible values of x now find all the ones that work, and you have all solutions
 one year ago
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