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Thread: Triganometry , Help please

  1. #1
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    Triganometry , Help please

    Hi, could someone tell what what i need to do to answer these q's please, thank you

    All the angles are in interval -180degrees to 180degrees.
    So , given that sina<0 and cos a =0.5 find a.

    Im not sure what to do, so any help is great thank you all.
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Chez_ View Post
    Hi, could someone tell what what i need to do to answer these q's please, thank you

    All the angles are in interval -180degrees to 180degrees.
    So , given that sina<0 and cos a =0.5 find a.

    Im not sure what to do, so any help is great thank you all.
    The reference angle is $\displaystyle \frac{\pi}{3}$. And a is in quadrant IV. So what is a?

    -Dan
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  3. #3
    Senior Member topher0805's Avatar
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    First we need to find a reference angle. To do this, find $\displaystyle cos \frac {1}{2}$.

    Recall the special triangle with sides 1, 2, and $\displaystyle \sqrt {3}$.



    Where n is equal to any number. In this case, n is 1.

    Cosine is equal to adjacent over hypotenuse, so in this case:

    $\displaystyle cos \frac {1}{2}$

    The adjacent side must be 1 and the hypotenuse must be 2. What angle in this triangle represents that? The 60 degree angle, or $\displaystyle \frac {\pi}{3}$ in radians.

    So, $\displaystyle cos \frac {1}{2}$ is equal to $\displaystyle \frac {\pi}{3}$.

    Now that we have our reference angle, think about the quadrants. We know that $\displaystyle sin a$ is less than zero and therefore negative, so which quadrants are $\displaystyle sin$ negative in? The third and fourth quadrants.

    Recall that sin is a periodic function, repeating every $\displaystyle 2\pi$.

    So, the values of a that satisfy this equation are:

    $\displaystyle 2n\pi + \frac {\pi}{3}$, where n is any integer.

    For which values of n does this equation fall into the third or fourth quadrant? The only correct answer is 1.

    So, your final answer is:

    $\displaystyle 2\pi + \frac {\pi}{3}$

    $\displaystyle = \frac {7\pi}{3}$
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