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Thread: Related Acute Angle

  1. #1
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    Related Acute Angle

    Hi,

    I hope someone can help. I'm trying to understand why the equivalent expression in terms of the related acute angle for sec(7pi/6) is -sec(pi/6). I understand why the answer is sec(pi/6), but I don't see why there is a negative sign in-front of the solution. Can someone please explain why?

    I'd really appreciate help

    Sincerely,
    Olivia
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  2. #2
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  3. #3
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    Re: Related Acute Angle

    Quote Originally Posted by otownsend View Post
    I hope someone can help. I'm trying to understand why the equivalent expression in terms of the related acute angle for sec(7pi/6) is -sec(pi/6). I understand why the answer is sec(pi/6), but I don't see why there is a negative sign in-front of the solution. Can someone please explain why?
    1. Do you understand that $\cos\left(\theta\right)=\cos\left(\theta-2\pi\right)$ You said you did$~??\\$
    2. Do you understand that $\cos\left(\theta\right)$ is an odd function, $\cos\left(-\theta\right)=-\cos\left(\theta\right)\\$
    3. Do you understand that $\sec\left(\theta\right)$ is $\frac{1}{\cos\left(\theta\right)}\\$
    4. Does it follow that on its domain $\sec(x)$ is an odd function? $\sec(-x)=-\sec(x)$
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  4. #4
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    Re: Related Acute Angle

    I understand #1.

    I don't understand #2. I thought that cosine is an even function and sine is an odd function. Is this different?

    I understand #3.

    In order to understand #4, I probably need an explanation on #2.
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    Re: Related Acute Angle

    Quote Originally Posted by otownsend View Post
    I understand #1.

    I don't understand #2. I thought that cosine is an even function and sine is an odd function. Is this different?

    I understand #3.

    In order to understand #4, I probably need an explanation on #2.
    You are correct. I just mixed the two up. sorry about that.

    $\frac{{7\pi }}{6} - 2\pi = - \frac{{5\pi }}{6} \in III$

    Cosine & hence secant are negative in III. The reference angle is $\frac{{1\pi }}{6}$

    But being in III makes the answer $-\sec\left(\frac{{1\pi }}{6}\right)$
    Last edited by Plato; May 12th 2017 at 10:30 AM.
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  6. #6
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    Re: Related Acute Angle

    Makes sense. Thanks!
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