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

2 sin^2x = sin x

Question

Find all solutions in the interval [0, 2π).

2 sin^2x = sin x

anonymous · Answer

double angle formula

set equal to zero
factor

solve for x

anonymous · Answer

i dont know how to use the double angle formula @completeidiot

anonymous · Answer

its a trig identity

$$\sin(2x) = 2sinxcosx$$

anonymous · Answer

ok and what do i do after that?

anonymous · Answer

substitute.... then follow above steps

anonymous · Answer

substitute what ? @completeidiot

anonymous · Answer

double angle formula...

anonymous · Answer

could you explain a little more on how to do that ? @completeidiot

anonymous · Answer

oh crap, misread the problem, you dont need to use double angle formula

anonymous · Answer

just set equal to zero, factor, then solve

anonymous · Answer

If your problem was

2sin(2x) = sin x

then substituting using double angle formula would be 

2 ( 2sin x cos x)) = sin x

anonymous · Answer

ok so $$2SIN^2X-SINX=0$$ ?

anonymous · Answer

now factor

anonymous · Answer

factor what ? @completeidiot

anonymous · Answer

look at the equation and tell me if you are capable of factoring anything out

anonymous · Answer

from my equation i got $$2\sin^2x-sinx=0$$
and then i got $$sinx(2\sin-1)$$
@completeidiot

anonymous · Answer

right

and that expression is equal to zero


now use the zero property of multiplication

basically it means either sinx =0 or 2 sin x -1 = 0

solve for x in both cases

anonymous · Answer

i got x=0 and sinx=1/2 @completeidiot

anonymous · Answer

just saying, there should be 4 different answers

i suggest looking a unit circle

anonymous · Answer

so im guessing the answers are 0, pie, pie/6 , & 5pie/6 ? @completeidiot

anonymous · Answer

looks about right