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Thread: Please Help me Solve 0-3+3cos(a/3)=-1/(sin(a/3)) * (9-a)

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    Exclamation Please Help me Solve 0-3+3cos(a/3)=-1/(sin(a/3)) * (9-a)

    Please Help me Solve this hard Maths equation for a

    0-3+3cos(a/3)=-1/(sin(a/3)) * (9-a)

    I have no idea how to do the working out and the answer for a is supposed to be a=5.41

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    Quote Originally Posted by Danie View Post
    Solve ... for a

    0-3+3cos(a/3)=-1/(sin(a/3)) * (9-a)

    ... a is supposed to be a=5.41
    Rounded to two places, 5.41 is one of the three solutions.

    We can simplify the expressions above, by making a substitution.

    Let k = a/3 (so a = 3*k)

    This substitution leads to an equivalent equation:

    1 - cos(k) = (3 - k)/sin(k)

    Using an identity for sin(2*k) we also get:

    sin(k) - 1/2*sin(2*k) = 3 - k

    Graphing both sides of either of these equations shows three solutions for k (see below). Tripling each of these solutions yields the solutions for a.

    When we have an equation comprised of a trigonometric function set equal to a polynomial function, it is often impossible to solve by hand.

    I approximated the three solutions for k, by zooming in on the intersection points of a graph. One could also use a Computer Algebra System, to approximate the solutions.

    There are methods for approximating by hand; have you heard of Newton's Method?
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    I havent heard of Newtons method.

    Is there anyway just to end up at 5.41 through algebra only.

    Thanks

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    Elite Member mmm4444bot's Avatar
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    Quote Originally Posted by Danie View Post
    Is there anyway just to end up at 5.41 through algebra only.
    No. Your equation relates a trigonometric function (transcendental) to a linear function (polynomial). There's no closed-form approach, for finding solutions; we need to approximate the three solutions, using an iterative process of some sort.

    Google the following, for more information:

    difference between polynomial and transcendental equation
    "English is the most ambiguous language in the world." ~ Yours Truly, 1969

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    ok thankyou

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