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Thread: Equivalent expressions for values of cot and sec.

  1. #1
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    Equivalent expressions for values of cot and sec.

    Hello everyone, I do not understand what the question is asking nor do i understand how to do this, perhaps someone could help me?

    1. Determine an equivalent expression in terms of the related actue angle

    a) cot(-π/4) --answer is cot 3π /4

    b) sec7π /6 --answer is sec5π /6


    Thanks!
    Last edited by mr fantastic; Nov 15th 2009 at 01:57 AM.
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  2. #2
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    Hello TheCB4
    Quote Originally Posted by TheCB4 View Post
    Hello everyone, I do not understand what the question is asking nor do i understand how to do this, perhaps someone could help me?

    1. Determine an equivalent expression in terms of the related actue angle

    a) cot(-π/4) --answer is cot 3π /4

    b) sec7π /6 --answer is sec5π /6


    Thanks!
    An acute angle is one that is between $\displaystyle 0$ and $\displaystyle \pi/2$, so both of these answers are incorrect, as the angles are greater than $\displaystyle \pi/2$.

    The first one should be $\displaystyle -\cot(\pi/4)$ and the second is $\displaystyle -\sec(\pi/6)$.

    I think you should study the graphs of $\displaystyle y = \cot x$ and $\displaystyle y =\tan x$. For example, just here.

    From these, you can work out (among other things) that
    $\displaystyle \cot(-x) =-\cot (x)$ (which I used to answer question 1)
    and
    $\displaystyle \sec(\pi+x)=-\sec(x)$ (which I used to answer question 2)
    Grandad
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