Question

2sin(^2)x + sinx=0

How do I at least start off with this question?

Answer 1

Do you mean? \[2Sin^2(x)+Sin(x)=0\]

Answer 2

are you taking the derivative, graphing it, or what?

Answer 3

imer - Yes yes, how do I write it out like that?

And sorry, forgot to mention that I need to solve it.

Answer 4

What if I say;\[2x^2+x=0\]Will you be able to solve it?

Answer 5

I honestly do not know. I don't know if it is because my brain is fried or what. If it helps, I am working with periodic functions, the previous questions I have been working with are simpler to calculate the solution/s.

Answer 6

Let start with an easy example;\[x^2+x=0\]Do you see anything common in "x^2" and "x"?

Answer 7

That they are both divisible by x?

Answer 8

Correct, means they have "x" in common so can you factorize it for me?

Answer 9

\[(x^1*x^1)+x^1=0\]

Answer 10

You can see they have "x^1" which is "x" in common, so I can write it as \[x^1(x^1+1)=0\]right?

Answer 11

Yep!

Answer 12

Ok, now lets take it further\[2x^2+x=0\]Can you factorize it for me?

Answer 13

Would it just be as simple as x(2x + 1) = 0 ?

Answer 14

correct!, Now lets replace "x" with Sin(x)

Answer 15

\[2Sin^2(x)+Sin(x)=0\]Can you please factorize it for me once again?

Answer 16

I want to say sinx(2sinx + 1) = 0
But would that then make it 2sinx^2, rather than 2sin(^2)x?

Answer 17

\[Sin^2(x)=[Sin(x)]^2\]Don't be confused!

Answer 18

So it would be sin(2sinx + x) = 0 ?

Answer 19

Almost correct but you made a mistake "sin(x)(2sinx + x) = 0" instead of "sin(2sinx + x) = 0"

Answer 20

You replaced "x" in Sin(x) by "2sinx + x" but it not the same as "sin(x)(2sinx + x) = 0"

Answer 21

\[Sin(x)[2Sin(x)+1] \neq Sin([2Sin(x)+1])\]

Answer 22

Its easy.. Just don't confuse between Sin^2X and (SinX)^2.. They meant the same

Answer 23

Okay, I get where that comes from

Answer 24

Now what you think should be the next step?

Answer 25

Read my attachment it MAY help...And don't laugh on my writing.
:P

Answer 26

@Yajnesh_Joglekar It might help him, but I would like to help by forwarding you to this link http://openstudy.com/code-of-conduct

Answer 27

Oh I am sorry.. U knoe m new to this stuff.. So I didn't Know.. Apologies..

Answer 28

I did try and understand all the steps in the image, but I don't see how it goes straight to sinx = 0 ... But I think my brain just may have clicked on so give me a second to scribble it down in my book xD

Answer 29

Well.. It should be with your intuition.. If A*B=0.. then either A=0 or B=0 OR BOTH OF THEM ARE 0

Answer 30

Sorry, lost internet just before posting my response:

"Okay so looking at the image that Yajnesh_Joglekar posted, that sort of helped.
Both sides divide by sinx, giving (2sinx + 1) = 0
Move the +1 to the other side, giving 2sinx = -1
Divide both sides by 2, giving sinx = -1/2

And providing that is all right then I know where to go from there"

Answer 31

Good Luck..
SYA