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Thread: Find all solutions

  1. #1
    Member purplec16's Avatar
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    Find all solutions

    How do you find the solutions? I dont really want to know the solution, I just need to know how you would calculate it for this type of problem.
    $\displaystyle cos\theta=\frac{1}{sec\theta}$

    $\displaystyle cos\theta sec\theta=1$

    Is this right so far?, what is my next step
    Last edited by purplec16; Mar 9th 2010 at 05:37 PM. Reason: Tried to work it out again, but did not get it
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  2. #2
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    Quote Originally Posted by purplec16 View Post
    How do you find the solutions? I dont really want to know the solution, I just need to know how you would calculate it for this type of problem.
    $\displaystyle cos\theta=\frac{1}{sec\theta}$

    $\displaystyle cos\theta sec\theta=1$

    Is this right so far?, what is my next step
    This is not an equality that you can solve for $\displaystyle \theta$ with. It's an identity.

    In other words

    $\displaystyle \cos{\theta} = \frac{1}{\sec{\theta}}$ for ALL $\displaystyle \theta$, provided that the denominator does not equal $\displaystyle 0$.
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  3. #3
    Member purplec16's Avatar
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    I still dont get it so I have to solve it first then find the solutions?
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    Read my answer properly.

    ANY number $\displaystyle \theta$ will satisfy this equation because IT IS AN IDENTITY. (as long as the number $\displaystyle \theta$ doesn't make the denominator $\displaystyle = 0$.)
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    Quote Originally Posted by purplec16 View Post
    How do you find the solutions? I dont really want to know the solution, I just need to know how you would calculate it for this type of problem.
    $\displaystyle cos\theta=\frac{1}{sec\theta}$

    $\displaystyle cos\theta sec\theta=1$

    Is this right so far?, what is my next step
    Hi purplec16,

    $\displaystyle \frac{1}{cos\theta}$ is $\displaystyle sec\theta$

    "They" are equal for all $\displaystyle \theta $
    as they are one and the same.

    As $\displaystyle cos\theta$ ranges from -1 to 1 $\displaystyle sec\theta$ is never zero.
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  6. #6
    Member purplec16's Avatar
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    I thought the range of cos is 0 to 2pi?
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  7. #7
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    Hi purplec16,

    the angle $\displaystyle \theta$ ranges from 0 to $\displaystyle 2{\pi}$ over one period

    and $\displaystyle Cos\theta$ ranges from -1 to 1
    Attached Thumbnails Attached Thumbnails Find all solutions-cosa.jpg  
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