- anonymous

Find all solutions to the equation.
sin^2 x + sin x = 0

- chestercat

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- freckles

factor the sin^2(x)+sin(x)

- freckles

there is a sin(x) factor in each term

- anonymous

sin x (sin x + 1) = 0 ?

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## More answers

- freckles

yes
now set both factors equal to 0
sin(x)=0 or sin(x)+1=0

- freckles

so you have to solve both of those equations
sin(x)=0 or sin(x)=-1

- anonymous

sin x = 0 , 2pi
sin x = -1 would be x = 3pi/2 ?

- freckles

what about x=pi or x=0
sin(0)=?
sin(pi)=?

- anonymous

i get very confused by the unit circle :/

- freckles

When you look at the unit circle you are looking for when the y-coordinate is 0
since we are talking about sine
cos is the x-coordinate

- freckles

that is when we are solving sin(x)=0

- freckles

you already found all the solutions to sin(x)=-1 in the interval [0,2pi]

- anonymous

3pi/2 is the only solution to sin x = -1 ?

- freckles

sin(x)=0 when x=0,pi,2pi
those are the solutions in [0,2pi]
There are infinitely many more solutions outside that interval

- freckles

yes sin(x)=-1 has solution x=3pi/2
only if we are looking at [0,2pi]

- freckles

As I said though if we aren't restricted to this interval then there are infinitely many solutions.

- anonymous

okay, i understand now.

- freckles

Your question says to find all the solutions.

- freckles

so it seems we are restricted to the interval [0,2pi]

- freckles

what did you notice about the solutions to sin(x)=0
like we had solutions 0pi,1pi,2pi,...continuing this pattern
you should be able to say in general the solutions to sin(x)=0
is npi where n is an integer

- anonymous

multiples of 2pi right?

- freckles

sin(x)=-1 you said had solution x=3pi/2
to include all the solutions you could recall the period of sin is 2pi
and say the solutions to sin(x)=-1 are x=3pi/2+2pi*n
where again n is an integer

- freckles

well to the first equation sin(x)=0
the answers are multiples of pi

- freckles

you say the solution is sin(x)=0
is x=2npi
you are excluding odd n..because the 2 in front of the n makes it is even for any n
for example x=2npi doesn't include the solution x=pi

- freckles

so you do have to include all the solutions to sin(x)=0
we say the solutions are x=npi
where n is an integer

- anonymous

okay, i see now

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