Question

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

sin2x + sin x = 0

Answer 1

Use the double angle formula on sin2x. Then you can factor and set the two factors equal to 0.

Answer 2

I got that far but don't know what to do after that

Answer 3

I know that sinx=0 or sinx-1=0

Answer 4

and now im stuck

Answer 5

and then what

Answer 6

at pi and 2pi but that isn't an option

Answer 7

i put 4pi/3 and 5pi/3 is that correct?

Answer 8

ohhh

Answer 9

3pi/2?

Answer 10

you mean sinx=-1 ?

Answer 11

at pi?

Answer 12

that's not in my options... 0 and pi are in each answer but each one shows either 3 or 4 solutions

Answer 13

are 4pi/3 and 5pi/2 solutions as well

Answer 14

Ah, I apologize, I made a silly mistake.

Answer 15

sin2x = 2sinxcosx.

Answer 16

2sinxcosx + sinx = 0 means
sinx(2cosx + 1) = 0
So we have:
sinx = 0
2cosx + 1 = 0

So the answers from sinx = 0 are okay, we just need to solve for 2cosx +1 = 0

Answer 17

So can we solve for 2cosx + 1 = 0?