trig

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how to do the calculation while taking 'A'
as 15 in the half angle formula used for calculating the value of sin 7.5 ?

  • trig -

    Unless you have found sin15 or cos15 before, and it has become part of your trig repertoire , you will have to do it twice

    since you must know that cos 30 = √3/2
    and using
    cos 2A = 2cos^2 A - 1 , let 2A = 30
    cos30 = 2cos^2 15 - 1
    solving this for cos 15 I got √(√3 + 2)/2

    now use the other expansion for cos 2A
    cos 2A = 1 - 2sin^2 A
    cos 15 = 1 - 2sin^2 7.5
    this gave me
    2sin^2 7.5 = 1 - √(√3 + 2)/2
    sin 7.5 = √[2 - √(√3 + 2) ]/2

    you can check it with sin 7.5 on your calculator, it is correct.

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