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Math Help - easy trigonometric function

  1. #1
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    easy trigonometric function

    given that sec 60 degree=2 find the sec 20 degree without using a calculator..i know this is easy question,but i dont know how to get the answer..please help!
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  2. #2
    MHF Contributor
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    Quote Originally Posted by mastermin346 View Post
    given that sec 60 degree=2 find the sec 20 degree without using a calculator..i know this is easy question,but i dont know how to get the answer..please help!
    this reply is a bit late but you might still be interested to know the solution and it's not easy .

    sec 60 =2

    cos 60=1/2

    Do you know the triple angle formula ,

    cos 3x =4cos^3 x -3cos x

    Substitute x=20 ,

    cos 3(20)=4cos^3 20- 3cos 20

    1/2=4cos^3 20-3 cos 20

    8cos^3 20-6cos 20-1=0

    Solving this ,

    cos 20 = 0.94 , cos 20= -0.77(undefined) , cos 20 = -0.17 (undefined) --- since cos cant be -ve in the 1st quadrant

    sec 20 = 1/0.94

    sec 20 = 1.064
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  3. #3
    Junior Member mrmohamed's Avatar
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    Quote Originally Posted by mathaddict View Post
    this reply is a bit late but you might still be interested to know the solution and it's not easy .

    sec 60 =2

    cos 60=1/2

    Do you know the triple angle formula ,

    cos 3x =4cos^3 x -3cos x

    Substitute x=20 ,

    cos 3(20)=4cos^3 20- 3cos 20

    1/2=4cos^3 20-3 cos 20

    8cos^3 20-6cos 20-1=0

    Solving this ,

    cos 20 = 0.94 , cos 20= -0.77(undefined) , cos 20 = 0.17 (undefined)

    sec 20 = 1/0.94

    sec 20 = 1.064
    HI all
    good work mathaddict but how u find it without calculator!!!!!
    given that sec 60 degree=2 find the sec 20 degree without using a calculator
    mrmohamed
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