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

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lgbasallote
 3 years ago
Best ResponseYou've already chosen the best response.0i suppose the only way for this to happen is if the x were 0....

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

lgbasallote
 3 years ago
Best ResponseYou've already chosen the best response.0hmm i suppose pi works

lgbasallote
 3 years ago
Best ResponseYou've already chosen the best response.0sin 2x = sin x arcsin both sides 2x = x 2x  x = 0 x = 0 how can i get the other values?

leedomathgeek
 3 years ago
Best ResponseYou've already chosen the best response.1sin(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

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

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

lgbasallote
 3 years ago
Best ResponseYou've already chosen the best response.0because one angle is missing

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

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

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

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

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

leedomathgeek
 3 years ago
Best ResponseYou've already chosen the best response.1is the 5th solution

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

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

apple_pi
 3 years ago
Best ResponseYou've already chosen the best response.0Here'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
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