Sum-to-Product

Discussion in 'Geometry and Trigonometry' started by nycmathguy, Jan 2, 2022.

  1. nycmathguy

    nycmathguy

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    Section 5.5

    Screenshot_20211231-174544_Samsung Notes.jpg

    IMG_20220102_155629.jpg

    IMG_20220102_155641.jpg
     
    nycmathguy, Jan 2, 2022
    #1
  2. nycmathguy

    MathLover1

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    sin(3theta)+sin(theta)

    sin(u)+sin(v) =2sin(u/2 + v/2) cos(u/2 - v/2) where u=3theta and v=theta

    =2sin(3theta/2 + theta/2) cos(3theta/2 - theta/2)

    =2sin(2theta) cos(theta).......sin(2theta)=2sin(θ) cos(θ)

    =2(2sin(θ) cos(θ)) cos(theta).

    =4sin(θ) cos^2(θ)
     
    MathLover1, Jan 2, 2022
    #2
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  3. nycmathguy

    nycmathguy

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    Wrong again, right?
    If so, I may do 53 and 55.
     
    nycmathguy, Jan 3, 2022
    #3
  4. nycmathguy

    nycmathguy

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    IMG_20220103_211811.jpg

    IMG_20220103_211822.jpg

    IMG_20220103_211835.jpg
     
    nycmathguy, Jan 4, 2022
    #4
  5. nycmathguy

    MathLover1

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    53. correct, you can just stop on line 2 sin( θ) cos(4 θ), no need to go further
    55. correct
     
    MathLover1, Jan 4, 2022
    #5
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  6. nycmathguy

    nycmathguy

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    Thank goodness I got it right.
     
    nycmathguy, Jan 4, 2022
    #6
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