Chapter 12.2, Problem 8OE

To determine

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

  $\cos \theta =\sin 45°$

Answer to Problem 8OE

  $\theta =45°$

Explanation of Solution

Given:

  $\cos \theta =\sin 45°$

Formula Used:

  $\sin \theta =\cos \left(90°-\theta \right)$

Calculation:

  $\begin{array}{l}\cos \theta =\sin 45°\\ \Rightarrow \cos \theta =\cos \left(90°-45°\right)\mathrm{...........}[\sin \theta =\cos \left(90°-\theta \right)]\\ \Rightarrow \cos \theta =\cos 45°\\ \Rightarrow \theta =45°\mathrm{.................................}[\cos x=\cos y\iff x=y\text{ in first quadrant]}\end{array}$