Question

Medal rewarded!

Find all solutions to the equation.
sin^2x + sin x = 0

Answer 1

@hartnn Sorry to bother you, but you explain everything the best!

Answer 2

@OtonoGold i still dont understand what the answer would be

Answer 3

using the identity sin (2x) = 2 sin x cos x

So that would make your original equation

2 cos x sin x + sin x = 0,
or 2 cos x sin x = -sin x

Answer 4

factor out sin x from left , what u get ?

Answer 5

Just approach this like you would any old quadratic formula solving for x:

ax^2+bx+c=0

except instead of x's you have sinx's that you're solving for.

Answer 6

sinx (sinx+1) = 0
sinx = 0
sinx = -1
solve for x

Answer 7

Can one of you please lay it all out in one comment so i can see the steps?

Answer 8

So originally you determined

sin(x) = 0
sin(x) = -1 So Then ALL solutions would be:
0+360∘n,90∘+360∘n,180∘+360∘n

Answer 9

Get it kinda of ?

Answer 10

Kind of
so this is all you have to do?
sin(x) = 0
sin(x) = -1 So Then ALL solutions would be:
0+360∘n,90∘+360∘n,180∘+360∘n

Answer 11

@hartnn

Answer 12

2 cos x sin x + sin x = 0,
or 2 cos x sin x = -sin x
sinx (sinx+1) = 0
sinx = 0
sinx = -1
So Then ALL solutions would be:
0+360∘n,90∘+360∘n,180∘+360∘n