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

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

lgbasallote Group TitleBest ResponseYou've already chosen the best response.0
hmm i suppose pi works
 2 years 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?
 2 years ago

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

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

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

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

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

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

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

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

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

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

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

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