Given the following information about one trigonometric function, evaluate the other five functions.

$\mathrm{cos}u=\frac{5}{13}$ , where $0\le u\le \frac{\pi}{2}.$

opatovaL
2021-02-09
Answered

Given the following information about one trigonometric function, evaluate the other five functions.

$\mathrm{cos}u=\frac{5}{13}$ , where $0\le u\le \frac{\pi}{2}.$

You can still ask an expert for help

svartmaleJ

Answered 2021-02-10
Author has **92** answers

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.

$\mathrm{tan}u=\frac{\mathrm{sin}u}{\mathrm{cos}u}$

$=\frac{\frac{12}{13}}{\frac{5}{13}}$

$=\frac{12}{5}$

$\mathrm{sec}u=\frac{1}{\mathrm{cos}u}$

$=\frac{1}{\frac{5}{13}}$

$=\frac{13}{5}$

$\mathrm{cos}ecu=\frac{1}{\mathrm{sin}u}$

$=\frac{1}{\frac{12}{13}}$

$=\frac{13}{12}$

$\mathrm{cot}u=\frac{1}{\mathrm{tan}u}$

$=\frac{1}{\frac{12}{5}}$

$=\frac{5}{12}$

Given,

We have identity

Therefore,

Now, finding other trigonometric function.

Jeffrey Jordon

Answered 2021-12-14
Author has **2313** answers

Answer is given below (on video)

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