Question

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

(sin x)(cos x) = 0

Answer 1

well where does sinx=0 and cosx=0?

Answer 2

I dont know how to start this.

Answer 3

as sinx*cosx=0
it means either sinx=0 or cosx=0
sinx=0 or cosx=0
x=npi or x=(2n+1)pi/2
put n=0,1,2,3
you get
x=0,pi or x=pi/2,3pi/2
take union
hence x=0,pi/2,pi,3pi/2

Answer 4

Ok how does "x=npi or x=(2n+1)pi/2"

Answer 5

see sinx=0 in 0,pi,2pi,3pi therefore it is being generalized as npi
and cosx=0 in pi/2,3pi/2,5pi/2 hence it is also generalized to (2n+1)pi/2

Answer 6

Alright Ill take not of that thank you

Answer 7

note*

Answer 8

welum