Chapter 7.3, Problem 13CFU

To determine

To simplify: the expression using an identity.

Answer to Problem 13CFU

  $V=-\cos \left(n{\omega }_{0}t\right)$

Explanation of Solution

Given information:

The voltage (let’s assume $V$ ) is expressed as follows:

  $V=\sin \left(n{\omega }_{0}t-90°\right)$

Here $n$ is positive integer ${\omega }_0$ is frequency of voltage and

  $t$ is time.

Calculation:

Use difference identity of sine to simplify the given expression as shown below.

  $\begin{array}{c}V=\sin \left(n{\omega }_{0}t-90°\right)\\ =\sin \left(n{\omega }_{0}t\right)\cos 90°-\cos \left(n{\omega }_{0}t\right)\sin 90°\\ =\sin \left(n{\omega }_{0}t\right)\left(0\right)-\cos \left(n{\omega }_{0}t\right)\left(1\right)\\ =-\cos \left(n{\omega }_{0}t\right)\end{array}$

Thus the simplified equation of voltage is $V=-\cos \left(n{\omega }_{0}t\right)$ .