Question

Find all solutions in the interval [0, 2π).
2sin^2x = sin x

I'm soo lost..

Answer 1

what do i do after i get to pi/6?

Answer 2

2sin^2x - sin x = 0
factor out sin x

Answer 3

sin x (2sin x-1) = 0


sin x = 0 for which angles of x ?

sin x = 1/2 for which angles of x ?

Answer 4

.....?

Answer 5

i said sinx = 1/2 at pi/6

Answer 6

now what do i do? i don't understand what it means to = 0? i didn't think it did... idk

Answer 7

sin x can be 0 too, right ?
so, x can take values of 0 and pi too, isn't it ?

Answer 8

also, there are 2 values of x for which sin x = 1/2
pi/6 is one of them, what is other ?

Answer 9

uhm... 5pi/6

Answer 10

and just pi is an answer too?

Answer 11

5pi/6, yes!

so your 4 answers are
0, pi/6, pi, 5pi/6

Answer 12

didn't you get why sin x =0 can also be true ?

Answer 13

no i got all the other answers i just dont understand why it can equal 0

Answer 14

2sin^2x - sin x = 0
factor out sin x
sin x(2 sin x -1) = 0

when a b = 0
a=0 or b= 0

so, when
sin x(2 sin x -1) = 0

sin x = 0 or 2 sin x -1 = 0

and since sin x = 0, we get x = 0 , pi

Answer 15

ohhh okay thank you. i think i get it.