Calculus

Find the Taylor polynomialof order 5 appoximation to sin(1.5)

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  1. sinx = x - x^3/3! + x^5/5! - ...
    sin 1.5 = 1.5 - (1.5)^3/6 + (1.5)^5/120
    = 1.5 - .5625 + .06328 -
    = 1.00078

    my calculator said
    tan 1.5 = .997495

    so clearly 3 terms are not sufficient for good accuracy, (sine can't have a value > 1)
    Taking one more term, -(1.5)^7/7! would bring it to .9974

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