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Math Help - trigonometric equation solve

  1. #1
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    trigonometric equation solve

    Are solving & proving the same thing? My book has a method for "proving" using either the quotient identity or pythagorean identity - you know that whole, LS=RS stuff.

    Earlier, though there is a method for "solving" by "let k=cos x" for example.

    Well, for some of my assignment, I used the "solving" method *because the question told me to solve* and when it was returned to me, the teacher's notes were:

    your factoring is rushed and solving is based on two identities: the tangent and sin^2x+cos^2x=1. You will be able to solve all by using these two.


    I don't know what is going on.
    If anyone can point me to a nice basic thread on MHP/website on this stuff I will be ever-so grateful!
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  2. #2
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    Quote Originally Posted by sux@math View Post
    Are solving & proving the same thing? My book has a method for "proving" using either the quotient identity or pythagorean identity - you know that whole, LS=RS stuff.

    Earlier, though there is a method for "solving" by "let k=cos x" for example.

    Well, for some of my assignment, I used the "solving" method *because the question told me to solve* and when it was returned to me, the teacher's notes were:

    your factoring is rushed and solving is based on two identities: the tangent and sin^2x+cos^2x=1. You will be able to solve all by using these two.

    I don't know what is going on.
    If anyone can point me to a nice basic thread on MHP/website on this stuff I will be ever-so grateful!
    Suppose I asked you to solve the equation 2 \sin{^2}{x} + 3 \cos{^2}{x} = 3.

    You would have to use the identity \sin{^2}{x} + \cos{^2}{x} = 1.

    By example:
    2 \sin{^2}{x} + 3 \cos{^2}{x} = 3

    2 \sin{^2}{x} + 2 \cos{^2}{x} + \cos{^2}{x} = 3

    (2 \sin{^2}{x} + 2 \cos{^2}{x}) + \cos{^2}{x} = 3

    2 + \cos{^2}{x} = 3

    \cos{^2}{x} = 1 etc.

    To prove the identity we used, we would have to employ the definition of the sine and cosine. But the difference between proving and solving is that proving is illustrating that a certain statement is always true, such as \sin{^2}{x} + \cos{^2}{x} = 1, whereas solving involves finding the values for the variables that satisfy a given equation. For the above, we have \cos{x} = -1 or \cos{x} = 1, giving us the answers x = -\pi + 2\pi{n} and x = 2\pi{n}.
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