anonymous
  • anonymous
Solve the following equation for theta where 0 < or= theta < 2 pie sin ^2 theta = sin theta
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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freckles
  • freckles
\[\sin^2(\theta)-\sin(\theta)=0\] factor left hand side
anonymous
  • anonymous
is that (sin theta) (sin theta)???
freckles
  • freckles
yes x^2 can be written as x*x

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anonymous
  • anonymous
so... now what?
freckles
  • freckles
factor
freckles
  • 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
  • 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
  • freckles
you try solving for sin(theta) now it is the same way
freckles
  • freckles
once you have solved for sin(theta) then you will easily be able to find theta
anonymous
  • anonymous
hold on, don't leave yet
anonymous
  • anonymous
sin =0 sin theta = 0
anonymous
  • anonymous
I have no idea what to do next
freckles
  • freckles
well you have one equation correct but you are missing an equation
freckles
  • freckles
have you not factored \[\sin^2(\theta)-\sin(\theta)\] yet?
freckles
  • freckles
do you see both sin^2(theta) and sin(theta) have a common factor?
freckles
  • 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
  • freckles
so you can factor that out of the expression
freckles
  • 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
  • freckles
you can use the unit circle to solve both equations
anonymous
  • anonymous
wait hold on
anonymous
  • anonymous
where did you get these 2 equations?
freckles
  • freckles
which two?
anonymous
  • anonymous
wait nvm
anonymous
  • anonymous
ok but how do you use the unit circle for this? i'm lost
freckles
  • freckles
do you know which equations you are solving?
anonymous
  • anonymous
sin^2 theta - sin theta = 0
freckles
  • freckles
you need to factor the left hand side
freckles
  • freckles
I have actually done this for you
anonymous
  • anonymous
I know x factor, but don't know how
freckles
  • freckles
|dw:1433565703539:dw|
freckles
  • freckles
now set both factors equal to 0
freckles
  • freckles
you have sin(theta)=0 or sin(theta)-1=0
freckles
  • freckles
find when sin(theta) is 0 on the unit circle find when sin(theta) is 1 on the unit circle
freckles
  • 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
  • anonymous
the answer is pie/2 and pie
anonymous
  • anonymous
but how is it pie though???
anonymous
  • anonymous
nvm
anonymous
  • anonymous
got it
freckles
  • 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
  • anonymous
ok thx

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