# Given the following information about one trigonometric function, evaluate the other five functions. cos u=5/13 , where 0 <= u <= pi/2.

Given the following information about one trigonometric function, evaluate the other five functions.
$\mathrm{cos}u=\frac{5}{13}$ , where $0\le u\le \frac{\pi }{2}.$
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svartmaleJ
Angle is in first quadrant and we know that in first quadrant all six trigonometric functions are positive.
Given, $\mathrm{cos}u=\frac{5}{13}$
We have identity ${\mathrm{sin}}^{2}x+{\mathrm{cos}}^{2}x=1$
Therefore,
$\mathrm{sin}u=\sqrt{1-{\mathrm{cos}}^{2}u}$
$=\sqrt{1-{\left(\frac{5}{13}\right)}^{2}}$
$=\sqrt{1-\frac{25}{169}}$
$=\sqrt{\frac{169-25}{169}}$
$=\sqrt{\frac{144}{169}}$
$=\frac{12}{13}$
Now, finding other trigonometric function.
$\mathrm{tan}u=\frac{\mathrm{sin}u}{\mathrm{cos}u}$
$=\frac{\frac{12}{13}}{\frac{5}{13}}$
$=\frac{12}{5}$
$\mathrm{sec}u=\frac{1}{\mathrm{cos}u}$
$=\frac{1}{\frac{5}{13}}$
$=\frac{13}{5}$
$\mathrm{cos}ecu=\frac{1}{\mathrm{sin}u}$
$=\frac{1}{\frac{12}{13}}$
$=\frac{13}{12}$
$\mathrm{cot}u=\frac{1}{\mathrm{tan}u}$
$=\frac{1}{\frac{12}{5}}$
$=\frac{5}{12}$
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