Chapter 13.8, Problem 4WE

To determine

To find:The trigonometric functionin a single angle.

Answer to Problem 4WE

The trigonometric function of a single angle is $\cos 2\pi$ .

Explanation of Solution

Given information:

The function is $2{\cos }^2\pi -1$

Calculation:

Consider the formula.

  $\cos \left(\alpha +\beta \right)=\cos \alpha \cos \beta -\sin \alpha \sin \beta$

Thus,

  $\begin{array}{c}2{\cos }^2\pi -1={\cos }^2\pi -\left(1-{\cos }^2\pi \right)\\ ={\cos }^2\pi -{\sin }^2\pi \\ =\cos \pi \cos \pi -\sin \pi \sin \pi \end{array}$

Apply the formula.

  $\begin{array}{c}\cos \pi \cos \pi -\sin \pi \sin \pi =\cos \left(\pi +\pi \right)\\ =\cos 2\pi \end{array}$