Question

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

sin2x + sin x = 0

Answer 1

@RadEn

Answer 2

@mustafa2014

Answer 3

sin(2x) + sin(x) = 0
2sin(x)cos(x) + sin(x) = 0
sin(x) (2cos(x) + 1) = 0
for the zeroes take each factor be equals zero then solve for x

sin(x) = 0
solve for x

2cos(x) + 1 = 0
cos(x) = -1/2
solve for x

Answer 4

so two would be 0,pi

Answer 5

and pi/3

Answer 6

so i got 0,pi,pi/3, and 5pi/3, right?

Answer 7

but that's not one of my options?

Answer 8

cos(5pi/3) = 1/2
i think there is typo in option, it should be 4pi/3

Answer 9

I am so confused..

Answer 10

the solution should be = {0, pi, 2pi/3, 4pi/3}

Answer 11

so thats wrong cause it's not one of my options?

Answer 12

@mustafa2014 did you get something else?