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anonymous

  • one year ago

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

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  1. freckles
    • one year ago
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    \[\sin^2(\theta)-\sin(\theta)=0\] factor left hand side

  2. anonymous
    • one year ago
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    is that (sin theta) (sin theta)???

  3. freckles
    • one year ago
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    yes x^2 can be written as x*x

  4. anonymous
    • one year ago
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    so... now what?

  5. freckles
    • one year ago
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    factor

  6. freckles
    • one year ago
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    \[x^2-x \\ x(x-1)\] you try factoring \[\sin^2(\theta)-\sin(\theta)\] it is the same way as I did the expression of x

  7. freckles
    • one year ago
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    \[x^2=x \\ x^2-x=0 \\ x(x-1)=0 \\ \text{ set both factors equal to zero } \\ x=0 \text{ or } x-1=0 \\ x=0 \text{ or } x=1 \]

  8. freckles
    • one year ago
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    you try solving for sin(theta) now it is the same way

  9. freckles
    • one year ago
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    once you have solved for sin(theta) then you will easily be able to find theta

  10. anonymous
    • one year ago
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    hold on, don't leave yet

  11. anonymous
    • one year ago
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    sin =0 sin theta = 0

  12. anonymous
    • one year ago
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    I have no idea what to do next

  13. freckles
    • one year ago
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    well you have one equation correct but you are missing an equation

  14. freckles
    • one year ago
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    have you not factored \[\sin^2(\theta)-\sin(\theta)\] yet?

  15. freckles
    • one year ago
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    do you see both sin^2(theta) and sin(theta) have a common factor?

  16. freckles
    • one year ago
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    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)

  17. freckles
    • one year ago
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    so you can factor that out of the expression

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

  19. freckles
    • one year ago
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    you can use the unit circle to solve both equations

  20. anonymous
    • one year ago
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    wait hold on

  21. anonymous
    • one year ago
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    where did you get these 2 equations?

  22. freckles
    • one year ago
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    which two?

  23. anonymous
    • one year ago
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    wait nvm

  24. anonymous
    • one year ago
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    ok but how do you use the unit circle for this? i'm lost

  25. freckles
    • one year ago
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    do you know which equations you are solving?

  26. anonymous
    • one year ago
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    sin^2 theta - sin theta = 0

  27. freckles
    • one year ago
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    you need to factor the left hand side

  28. freckles
    • one year ago
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    I have actually done this for you

  29. anonymous
    • one year ago
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    I know x factor, but don't know how

  30. freckles
    • one year ago
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    |dw:1433565703539:dw|

  31. freckles
    • one year ago
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    now set both factors equal to 0

  32. freckles
    • one year ago
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    you have sin(theta)=0 or sin(theta)-1=0

  33. freckles
    • one year ago
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    find when sin(theta) is 0 on the unit circle find when sin(theta) is 1 on the unit circle

  34. freckles
    • one year ago
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    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

  35. anonymous
    • one year ago
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    the answer is pie/2 and pie

  36. anonymous
    • one year ago
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    but how is it pie though???

  37. anonymous
    • one year ago
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    nvm

  38. anonymous
    • one year ago
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    got it

  39. freckles
    • one year ago
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    so you don't get that sin(pi)=0? also sin(0)=0 so I think you mean you have 0,pi/2,pi

  40. anonymous
    • one year ago
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    ok thx

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