Question

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

sin2x + sin x = 0

Answer 1

Do you know what's the identity for sin2x?

Answer 2

noo i forgot..

Answer 3

sin2x=2sinxcosx

Answer 4

So how do you proceed?

Answer 5

2sinx+cosx+sinx=0 right?
what do i do next?

Answer 6

no, it should be from
sin2x + sin x = 0
to
2sinxcosx + sin x =0 right?

Answer 7

ohh yea

Answer 8

you should try factoring now

Answer 9

sinx(2cosx+1)=0 is this right?
what do i do next? o.O

Answer 10

ya u r right :)

Answer 11

yes, now you can let
sinx=0 and 2cosx+1=0
then find the x values

Answer 12

equate that to 0 and find x values

Answer 13

so i got cosx=-1/2
how do i find the value of x?

Answer 14

well you can do this
cosx=-1/2
x=cos^{-1} (-1/2)

Answer 15

so what are all possible values of x? 0 and......what else O.o

Answer 16

@hannahg :) instead of o.O

Answer 17

no its not 0

Answer 18

@AravindG :)

Answer 19

you calculate cos^(-1) 1/2 first without minus on half
you'll get 60 degrees

Answer 20

yes:)

Answer 21

then use this chart for cosine

we are looking at the minus side since we got minus half.
then
180-60=120 degrees
180+60=240 degrees

Answer 22

@hannahg thats better :)

Answer 23

yes. so all the possible solutions will be pi, pi/3, 2pi/3?

Answer 24

you still have sinx=0 to do

Answer 25

yes......! so 0?

Answer 26

yes but dont forget about 180

Answer 27

since theta is 0, then you get 180

Answer 28

@.Sam. so what are all solutions in the interval??