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I get the concepts about all six $(\sin, \cos, \tan, \csc, \sec, \cot$). I'm just having trouble simplifying $\csc$ since I get $\frac{-3}{2\sqrt2}$, so how do i simplify?? Also, same for $\cot(t)$??

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To "simplify" $-\dfrac{3}{2\sqrt{2}}$, multiply top and bottom by $\sqrt{2}$.

Remark: In the bad old days, multiplication by a complicated number like $\sqrt{2}$ was unpleasant, and division by $\sqrt{2}$ was very unpleasant. So one automatically tried, if possible, to make denominators "nice." Note that with a calculator, your original form can be evaluated to high accuracy just as easily as the "simplified" form.

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  • $\begingroup$ Can you show me how to work it out? $\endgroup$
    – Xero1
    Sep 10, 2013 at 4:13
  • $\begingroup$ We get $-\dfrac{3}{2\sqrt{2}}\cdot\dfrac{\sqrt{2}}{\sqrt{2}}=-\dfrac{3\sqrt{2}}{4}$. $\endgroup$ Sep 10, 2013 at 4:18
  • $\begingroup$ Greatly appreciated, thank you! :) $\endgroup$
    – Xero1
    Sep 10, 2013 at 4:23
  • $\begingroup$ You are welcome. Now I am sure you can do $\cot$. $\endgroup$ Sep 10, 2013 at 4:24
  • $\begingroup$ Just to make sure, since tan(t): - 2sqrt2. Cot(t): - 1/2sqrt2 * sqrt2/sqrt2 = - sqrt2/4, correct? $\endgroup$
    – Xero1
    Sep 10, 2013 at 4:33

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