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Math:)

1. Evaluate tan[sin^-1(a)].
a. [sqrt(1-a^2)]/1-a^2
b. [sqrt(1-a^2)]/a
c. sqrt(1-a^2)
d. {a[sqrt(1-a^2)]}/1-a^2

I do not know the steps to find this answer and am not provided with a textbook. I have researched online some what, but I cannot seem to understand. Can someone please explain this?

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  1. draw the triangle. You want the angle whose sine is a = a/1
    so, pick an acute angle, and its opposite side is a, and the hypotenuse is 1.
    That means the adjacent side is √(1-a^2)

    so, tan(arcsin(a)) = opposite/adjacent = a/√(1-a^2)

    which, for those who insist on rational denominators, is (d)

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  2. Oh my goodness. This makes so much more sense than the extremely confusing lesson this is in. Thank you Steve!

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  3. right triangle sides a b c and angles A B C
    C is right, c is hypotenuse
    sin A = a/c
    let c = 1
    sin A = a
    a^2 + b^2 = 1 so b = sqrt(1-a^2)
    tan A = a/b = a/sqrt(1-a^2)
    multiply top and bottom by sqrt(1-a^2) to get rid of sqrt in denominator
    = a sqrt(1-a^2) / (1-a^2)

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