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Math Help - Solve the trigonometric equation?

  1. #1
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    Solve the trigonometric equation?

    a) Solve the following trigonometric equation: A = cosX + AsinX, for some angle X.

    b) The imaginary number i is equal to √-1. Use part a) to solve i = cosX + isinX.

    You will have used degrees to answer parts a and b. However, the mathematics below requires the use of radians. Convert degrees to radians by multiplying the degree measurement by π/180.

    You will now find a value of i^i.

    This will require the euler identity e^iX = cosX + isinX, part b) and exponent arithmetic.

    c) Evaluate, for one value, i^i.

    ----

    So I honestly have no idea how to start this off haha. Could someone help out? Obviously you don't need to solve the whole thing - i just need to know how to start it off. Thanks!
    Last edited by eleventhhour; May 24th 2014 at 01:39 PM.
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  2. #2
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    Re: Solve the trigonometric equation?

    Quote Originally Posted by eleventhhour View Post
    a) A = cosX + AsinX, for some angle X.
    b) The imaginary number i is equal to √-1. Use part a) to solve i = cosX + isinX.
    c) Evaluate, for one value, i^i.
    I honestly have no idea what parts (a & b) are about. I only taught the for thirty years.

    But I do know that $e^{(i\theta)}=\exp(i\theta)=\cos(\theta)+i\sin( \theta)$.

    And $i^i=\exp(i\log(i))=\exp(\frac{-\pi}{2})$
    Last edited by Plato; May 24th 2014 at 01:46 PM.
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  3. #3
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    Re: Solve the trigonometric equation?

    A = cosX + AsinX, for some angle X.

    Cos x = A ( 1- sin x )
    Cos2x/2 – sin2 x/2 = A ( cos x/2 – sin x/2 )2
    [Cos x/2 + sin x/2 ]/ [cos x/2 – sin x/2] = A
    [ 1 + tan x/2 ]/[ 1- tan x/2 ] = A

    1/[ tan ( π/4+ x/2 ) ] = A

    I am sure now you can finish it
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  4. #4
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    Re: Solve the trigonometric equation?

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    Karol
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