Question

Find all solutions to the equation.

sin^2 x + sin x = 0

Answer 1

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

Answer 2

there is a sin(x) factor in each term

Answer 3

sin x (sin x + 1) = 0 ?

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

i get very confused by the unit circle :/

Answer 9

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

Answer 10

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

Answer 11

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

Answer 12

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

Answer 13

sin(x)=0 when x=0,pi,2pi
those are the solutions in [0,2pi]

There are infinitely many more solutions outside that interval

Answer 14

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

Answer 15

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

Answer 16

okay, i understand now.

Answer 17

Your question says to find all the solutions.

Answer 18

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

Answer 19

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

Answer 20

multiples of 2pi right?

Answer 21

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

Answer 22

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

Answer 23

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

Answer 24

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

Answer 25

okay, i see now