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Math Help - Approximation Problems

  1. #1
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    Approximation Problems

    Help me please, I have no idea how to do these:
    1. Approximate the value of sin(32degrees)

    2. Use differentials to approximate Arctan 1.1

    Thank you!
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  2. #2
    Super Member Failure's Avatar
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    Quote Originally Posted by reiward View Post
    Help me please, I have no idea how to do these:
    1. Approximate the value of sin(32degrees)
    What about using \sin(32^\circ)=\sin(30^\circ + 2^\circ)=\sin(30^\circ)\cos(2^\circ)+\cos(30^\circ  )\sin(2^\circ)?
    You know the exact values of \sin(30^\circ) and \cos(30^\circ), and perhaps you also know that for small angles (expressed in radians) you have \sin(x)\approx x and \cos(x)\approx 1-x^2/2.
    So set x := 2^\circ/180^\circ \cdot \pi and plug those two approximations into the above expression for \sin(32^\circ).

    2. Use differentials to approximate Arctan 1.1
    Just use f(x)\approx f(x_0)+f'(x_0)\cdot (x-x_0), with x := 1.1, x_0 := 1, for f(x) := \arctan(x).
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