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ganeshie8 Group TitleBest ResponseYou've already chosen the best response.1
begin by subtractcting sinx both sides, and then factor sinx
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.1
\(2\sin x \cos x=\sin x \) subtract sinx both sides \(2 \sin x \cos x  \sin x = 0\) factor out sinx \(\sin x (2 \cos x  1) = 0 \)
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.1
We now have two factors whose product is zero, so the original equation will be satisfied when either factor is zero.
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.1
first set first factor = 0 => \(\sin x = 0\) the sin function 0, when \(x = 0 \) or \(x = \pi\) or \(x = 2\pi\)
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.1
similarly set the second factor = 0, and try getting other remaining solutions.
 2 years ago

johnnyalln Group TitleBest ResponseYou've already chosen the best response.0
I think i get this.. so the final answer would be x=0 or x=pi
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.1
not exactly thats half of the solutions only.. you need to set the second factor also equal to 0, and see what solutions u get
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.1
set second factor = 0 => \(2 \cos x 1 = 0\) \(\cos x = 1/2\) since, cos is positive in first and fourth quadrants : solution in first quadrant : \(x = \pi/3\) solution in fourth quadrant : \(x = 2\pi  \pi/3 = 5\pi/3\)
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.1
so, the solutions in interval \([0, 2\pi]\) are : \(0, \ \pi, \ \pi/3, \ 5\pi/3, \ 2\pi\)
 2 years ago

johnnyalln Group TitleBest ResponseYou've already chosen the best response.0
Got ya! I just got all of those except for 2pi..
 2 years ago

johnnyalln Group TitleBest ResponseYou've already chosen the best response.0
But yes makes perfect sense!
 2 years ago

johnnyalln Group TitleBest ResponseYou've already chosen the best response.0
Thanks a lot!
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.1
dw:1352555743690:dw
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.1
since we are looking for \(\sin x = 0\), we look at the graph of \(\sin\), see that the graph of \(\sin\) is becoming \(0\) when \(x = 0\) or \(x = \pi\) or \(x = 2\pi\) since all these 3 values of x are in the range \([0, 2\pi]\) , all 3 values satisfy the equation, and interval.
 2 years ago
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