Chapter 5 - Trigonometric Identities - Section 5.3 Sum and Difference Identities for Cosine - 5.3 Exercises - Page 220: 76c

$P = \frac{a}{r}~cos(ct)$

Let $r = n\lambda$ $P = \frac{a}{r}~cos(\frac{2\pi r}{\lambda}-ct)$ $P = \frac{a}{r}~cos(\frac{2\pi n\lambda}{\lambda}-ct)$ $P = \frac{a}{r}~cos(2\pi n-ct)$ $P = \frac{a}{r}[cos(2\pi n)~cos(ct)+sin(2\pi n)~sin(ct)]$ $P = \frac{a}{r}[(1)~cos(ct)+0]$ $P = \frac{a}{r}~cos(ct)$