Solve the following equation for theta where
0 < or= theta < 2 pie
sin ^2 theta = sin theta

- anonymous

Solve the following equation for theta where
0 < or= theta < 2 pie
sin ^2 theta = sin theta

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- freckles

\[\sin^2(\theta)-\sin(\theta)=0\]
factor left hand side

- anonymous

is that (sin theta) (sin theta)???

- freckles

yes x^2 can be written as x*x

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## More answers

- anonymous

so... now what?

- freckles

factor

- freckles

\[x^2-x \\ x(x-1)\]
you try factoring
\[\sin^2(\theta)-\sin(\theta)\]
it is the same way as I did the expression of x

- freckles

\[x^2=x \\ x^2-x=0 \\ x(x-1)=0 \\ \text{ set both factors equal to zero } \\ x=0 \text{ or } x-1=0 \\ x=0 \text{ or } x=1 \]

- freckles

you try solving for sin(theta) now
it is the same way

- freckles

once you have solved for sin(theta)
then you will easily be able to find theta

- anonymous

hold on, don't leave yet

- anonymous

sin =0
sin theta = 0

- anonymous

I have no idea what to do next

- freckles

well you have one equation correct
but you are missing an equation

- freckles

have you not factored \[\sin^2(\theta)-\sin(\theta)\]
yet?

- freckles

do you see both sin^2(theta) and sin(theta) have a common factor?

- freckles

as you said sin^2(theta) can be written as sin(theta)*sin(theta)
therefore sin(theta) and sin^2(theta) both have the common factor sin(theta)

- freckles

so you can factor that out of the expression

- freckles

\[\sin^2(\theta)-\sin(\theta)=0 \\ \sin(\theta)(\sin(\theta)-1)=0\]
that is what you should get for the left hand side after factoring
now set both factors equal to 0

- freckles

you can use the unit circle to solve both equations

- anonymous

wait hold on

- anonymous

where did you get these 2 equations?

- freckles

which two?

- anonymous

wait nvm

- anonymous

ok but how do you use the unit circle for this?
i'm lost

- freckles

do you know which equations you are solving?

- anonymous

sin^2 theta - sin theta = 0

- freckles

you need to factor the left hand side

- freckles

I have actually done this for you

- anonymous

I know x factor, but don't know how

- freckles

|dw:1433565703539:dw|

- freckles

now set both factors equal to 0

- freckles

you have sin(theta)=0 or sin(theta)-1=0

- freckles

find when sin(theta) is 0 on the unit circle
find when sin(theta) is 1 on the unit circle

- freckles

in other words you are looking for where the y-coordinate is 0 on the unit circle
and also looking for when the y coordinate is 1 on the unit circle

- anonymous

the answer is pie/2 and pie

- anonymous

but how is it pie though???

- anonymous

nvm

- anonymous

got it

- freckles

so you don't get that sin(pi)=0?
also sin(0)=0
so I think you mean you have 0,pi/2,pi

- anonymous

ok thx

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