Chapter 12.2, Problem 6OE

To determine

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

  $\tan \theta =\cot 70°$

Answer to Problem 6OE

  $\theta =20°$

Explanation of Solution

Given:

  $\tan \theta =\cot 70°$

Formula Used:

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

Calculation:

  $\begin{array}{l}\tan \theta =\cot 70°\\ \Rightarrow \tan \theta =\tan \left(90°-70°\right)\mathrm{...........}[\cot \theta =\tan \left(90°-\theta \right)]\\ \Rightarrow \tan \theta =\tan 20°\\ \Rightarrow \theta =20°\mathrm{.................................}[\tan x=\tan y\iff x=y\text{ in first quadrant]}\end{array}$