Question

Find all solutions to the equation.

sin2x + sin x = 0

Answer 1

@hartnn can you help me with this one?

Answer 2

is it sin squared x ? sin^2 x

Answer 3

Yes sorry about that, should be:
2 sin^2x = sin x

Answer 4

okay first we equate it to zero.

then we factor the Left hand side.

Answer 5

Okay, can you do everything at once so i can see each step by step? and then if i dont understand it i can ask for an explanation? Thanks

Answer 6

I just can't give answers, but don't worry I'll guide you :)

Answer 7

Well this is only a practice problem so its not like it counts towards anything, i have several other problems i can do on my own. It would really help me if it was all laid out how to do it and then i can do some on my own understanding it all.

Answer 8

Have you done any work so far?

Answer 9

Not on this problem.

Answer 10

I mean with the given practice problem.

Answer 11

okay first things first , we must equate it to 0

Answer 12

and then factor the left hand side.

Answer 13

if we equate 2 sin^2 x = sin x , it will be 2 sin ^2 x - sin x = 0

Answer 14

do you follow?

Answer 15

So far, yes

Answer 16

can you factor the left hand side?

Answer 17

TIP : think of sin^2 x as = x^2

Answer 18

Im not sure how to factor this one because of it saying sin and sin x?

Answer 19

okay for you not to be confused , think of

Answer 20

\[\sin^2x = x^2\]

Answer 21

sin x = x

Answer 22

Okay, but then whats there to factor?

Answer 23

Im sorry, see this is why it would be easier if you did it all step by step and then i ask questions

Answer 24

we can factor this out by taking out what is common, first substitute

Answer 25

\[2 \sin^2 x - \sin x \]

Answer 26

to ,

Answer 27

\[2 x^2 - x \]

Answer 28

then factor out what is common

Answer 29

the x's?

Answer 30

correcT :)

Answer 31

Okay so whats next? sorry im kind of in a hurry to finish this problem to do the rest

Answer 32

okay I'm just going to show you

Answer 33

x ( 2x -1 ) = 0

substitute x with sin x ( x = sin x , x^2 = sin^2 x )

sin x ( 2 sin x -1 ) = 0

sin x = 0 , .....................
2 sin x -1 = 0 ........... 2 sin x = 1 ,....... sin x = 1/2

Check by substition.

Answer 34

note in checking the we must equal both sides.

so , first 2 sin^2 x = sin x

2 ( 0 )^2 = 0 ,

2 (1/2)^2 = 1/2,

If both are equal its therefore the solution .

Answer 35

So the answer is 1/2?

Answer 36

is it only 1/2 ?

Answer 37

wait, 0, 1, and 1/2 right?

Answer 38

0 and 1/2 is the solution set.

Answer 39

Ohhhh i see it now

Answer 40

Be sure to learn it and practice :) I got to go bye :)

Answer 41

@yamyam70 did you solve this problem?
sin2x + sin x = 0

Answer 42

there is no such thing :)

Answer 43

should be , sin ^2 x + sin x = 0

Answer 44

This was the problem i needed solved, is this the problem we solved?

Find all solutions to the equation.

sin^2x + sin x = 0

Answer 45

Because earlier i replied incorrectly and said:
2 sin^2x = sin x

Answer 46

its the same thing, much easier, you can do it :)

Answer 47

No, im asking which one you solved.

Answer 48

Please go back to what I have solved earlier.

Answer 49

You solved this problem 2 sin^2 x = sin x , i needed this problem solved sin^z x = sin x

Answer 50

Sin^2 x = sin x*****

Answer 51

I had a typo and now we did the wrong problem :(

Answer 52

If you look closely.
There is no big difference between

2 sin^2 - sin x = 0
and
sin^2 - sin x = 0

Answer 53

now you have your example , please do sin^x - sin x = 0 :)

Answer 54

*sin^2x - sin x = 0

Answer 55

Okay i will, but can you tell me which one of these answers is correct for this problem:

Find all solutions in the interval [0, 2π).

2 sin2x = sin x

A. x = pi/3 , 2pi/3
B. x = pi/2 , 3pi/2 , pi/3 , 2pi/3
C. x = 0 , pi , pi/6 , 5pi/6
D. x = pi/6 , 5pi/6

Answer 56

We solved 2 sin^2x = sin x together but we didnt do it in the interval [0, 2π).