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Thread: Trig functions

  1. #1
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    Question Trig functions

    List the 6 trig functions of 90 degrees. Which does not represent a real number?

    I know what the 6 trig functions are...I just need help starting this problem. How would you set it up? Would you use the 30-60-90 triangle or the 45-45-90 triangle?

    Thanks for any help!
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  2. #2
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    Quote Originally Posted by live_laugh_luv27 View Post
    List the 6 trig functions of 90 degrees. Which does not represent a real number?

    I know what the 6 trig functions are...I just need help starting this problem. How would you set it up? Would you use the 30-60-90 triangle or the 45-45-90 triangle?

    Thanks for any help!
    There are 6 trig functions, but all of them are based around only 2... $\displaystyle \sin(x)$ and $\displaystyle \cos(x) $. You should be able to verify that $\displaystyle \sin(90) = 1 $ and $\displaystyle \cos(90) = 0 $

    And then remember that:

    $\displaystyle \tan(x) = \frac{\sin(x)}{\cos(x)} $

    $\displaystyle \text{cot}(x) = \frac{1}{\tan{x}} = \frac{\cos(x)}{\sin(x)} $

    $\displaystyle \text{sec}(x) = \frac{1}{\cos(x)} $

    $\displaystyle \text{cosec}(x) = \frac{1}{\sin(x)} $

    Hence:

    $\displaystyle \sin(90) = 1 $

    $\displaystyle \cos(90) = 0 $

    $\displaystyle \tan(90) = \frac{\sin(90)}{\cos(90)} = \frac{1}{0}$

    $\displaystyle \text{cot}(90) = \frac{\cos(90)}{\sin(90)} = \frac{0}{1}$

    $\displaystyle \text{sec}(90) = \frac{1}{\cos(90)} = \frac{1}{0} $

    $\displaystyle \text{cosec}(90) = \frac{1}{\sin(x)} = \frac{1}{1} $

    Can you evaluate which is real and which is undefined now?
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