Question

Find all solutions in the interval (0,2pi).
sin^2x + sin x = 0

Answer 1

sin x ( sin x + 1) = 0

sin x = 0 or -1

can u continue from here?

Answer 2

How did you get from the first equation to the second?

Answer 3

sin x is the Greatest common factor of sin^2 x and sin x

Answer 4

so we can take out sin x and divide by sin x to give the quotient in the brackets

Answer 5

this is called factoring

Answer 6

But with that answer you would get pi, 2pi, and 3pi/2.
The only options are:
x = 0, pi, 4pi/3, 5pi/3
x = 0, pi, pi/3, 2pi/3
x = 0, pi, pi/3, 5pi/3
x = 0, pi, 3pi/2

Answer 7

How did you get from
sin x (sin x + 1) = 0
to
sin x = 0 or -1
?

Answer 8

no when sin x = 0 , x = 0 , pi
sin x = -1 gives 3pi/2

Answer 9

when 2 functions a and b are multiplied together = 0 then a = 0 or b = 0

Answer 10

Oh, ok. I get it now. I made a simple mistake. Thank you!

Answer 11

yw