Key to "Given the following information about one trigonometric function,..."

opatovaL

Answered question

2021-02-09

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

\cos u = \frac{5}{13}

, where

0 \leq u \leq \frac{π}{2} .

svartmaleJ

Skilled2021-02-10Added 92 answers

Angle is in first quadrant and we know that in first quadrant all six trigonometric functions are positive.
Given,

\cos u = \frac{5}{13}

We have identity

\sin^{2} x + \cos^{2} x = 1

Therefore,

\sin u = \sqrt{1 - \cos^{2} u}

= \sqrt{1 - {(\frac{5}{13})}^{2}}

= \sqrt{1 - \frac{25}{169}}

= \sqrt{\frac{169 - 25}{169}}

= \sqrt{\frac{144}{169}}

= \frac{12}{13}

Now, finding other trigonometric function.

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

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

= \frac{12}{5}

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

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

= \frac{13}{5}

\cos e c u = \frac{1}{\sin u}

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

= \frac{13}{12}

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

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

= \frac{5}{12}

Jeffrey Jordon

Expert2021-12-14Added 2605 answers

Answer is given below (on video)

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