Chapter 12.2, Problem 18WE

To determine

Use the cofunction identities to find the measure of the acute angle $\theta$ .

  $\tan \varphi =\cot 17°$

Answer to Problem 18WE

  $\varphi =73°$

Explanation of Solution

Given:

  $\tan \varphi =\cot 17°$

Formula Used:

  $\cot \theta =\tan \left(90°-\theta \right)$

Calculation:

  $\begin{array}{l}\tan \varphi =\cot 17°\\ \Rightarrow \tan \varphi =\tan \left(90°-17°\right)\mathrm{...........}[\cot \theta =\tan \left(90°-\theta \right)]\\ \Rightarrow \tan \varphi =\tan 73°\\ \Rightarrow \varphi =73°\mathrm{.................................}[\tan x=\tan y\iff x=y\text{ in first quadrant]}\end{array}$