Find Exact Value of Trigonometric Expression...1

Discussion in 'Geometry and Trigonometry' started by nycmathguy, Dec 24, 2021.

  1. nycmathguy

    nycmathguy

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    Section 5.4

    Screenshot_20211221-014441_Samsung Notes.jpg

    IMG_20211224_104308.jpg

    IMG_20211224_104316.jpg

    IMG_20211224_104331.jpg

    IMG_20211224_104343.jpg

    IMG_20211224_104353.jpg

    IMG_20211224_104403.jpg

    1. Is there a shorter method that can be used? This is pretty tedious.

    2. Is my answer correct?
     
    nycmathguy, Dec 24, 2021
    #1
  2. nycmathguy

    MathLover1

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    1. yes, there is a shorter method

    use Angle-Sum and -Difference Identities

    sin(α + β) = sin(α) cos(β) + cos(α) sin(β)

    in your case α=pi/12 and β=pi/4

    sin(pi/12)cos(pi/4)+cos(pi/12)sin(pi/4)
    =sin(pi/12 + pi/4)
    =sin(π/3)
    =sqrt(3)/2

    2. as you can see, your answer is not correct
     
    MathLover1, Dec 24, 2021
    #2
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  3. nycmathguy

    nycmathguy

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    Ok. Thanks. I will do at least 2 more and post my work here.

    Christmas is here again. May your home be filled with laughter, contentment, harmony, peace, and an abundance of mercy. Happy holidays.
     
    nycmathguy, Dec 25, 2021
    #3
  4. nycmathguy

    nycmathguy

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    Take a look at 36.

    IMG_20211225_150604.jpg
     
    nycmathguy, Dec 25, 2021
    #4
  5. nycmathguy

    MathLover1

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    correct
     
    MathLover1, Dec 25, 2021
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  6. nycmathguy

    nycmathguy

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    Very good. Thank you.
     
    nycmathguy, Dec 26, 2021
    #6
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