Math

Use the half formula to find the exact value of the expression sin 22.5

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  1. one of the formulas for cos 2A is

    cos 2A = 1 - 2sin^2 A

    so if you let A = 22.5, then 2A = 45 and you should know the basic trig ratios for the 45º angle

    cos 45 = 1 - 2sin^2 22.5

    sin^2 22.5 = (1 - (√2)/2)/2

    take the square root again

    sin 22.5 = √[(1 - (√2)/2)/2]

    and there is your "exact" value

    check it with a calculator.

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  2. My options are

    -1/2 sqrt2 + sqrt2
    1/2 sqrt2 + sqrt-2
    -1/2 sqrt2 - sqrt2
    1/2 sqrt2 + sqrt2

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  3. none of those answers make any sense

    "-1/2 sqrt2 + sqrt2 " ----> that is sin 45º
    "1/2 sqrt2 + sqrt-2 " ----> sqrt-2 is undefined
    "-1/2 sqrt2 - sqrt2 " ----> that would be a negative result, the sin 22.5 is definitely positive
    "1/2 sqrt2 + sqrt2" ----> sine of any angle cannot be greater than 1, sqrt2 is already over 1

    by calculator
    sin 22.5 = .3826834
    evaluating my answer gives .3826834, I don't know why you doubt me.

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  4. I don't doubt you it doesn't make sense to me either but those are the choices I'm given let me look into this a little more and I'll re-post if need be

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