calculus

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evaluate tan^2 3.658

I know the answer is .322
but I don't know how to arrive at the answer.

  • calculus -

    I do not think so in either degrees or radians.

  • calculus -

    Most of us take the calculator and get the answer 0.322398.

    The fact that you asked how to get the answer suggests to me that you'd like to do the calculations yourself.

    You can do this by expansion of the tan(x) function which involves the evaluation of Bernoulli numbers. If we take advantage of the fact that 1+tan²(x)=sec(x)², or
    tan²(x)=sec(x)²-1
    we only need to evaluate cos(x), which is given algebraically as:
    cos(x)=1-x²/2!+x4/4!-....

  • calculus -

    additional note:
    Since tan(x)=tan(x±π), you can calculate tan(x-π) instead of tan(x).
    This way, the cosine series converges more rapidly.

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