Chapter 7 - Applications of Trigonometric Functions - Section 7.5 Simple Harmonic Motion; Damped Motion; Combining Waves - 7.5 Assess Your Understanding - Page 575: 33

Answer

(a) $f(x) =\frac{1}{2}cos(\frac{x}{2})-\frac{1}{2}cos(\frac{3x}{2})$ (b) See graph (red).

Work Step by Step

(a) $f(x)=sin(2x)sin(x)=\frac{1}{2}cos(\frac{2x-x}{2})-\frac{1}{2}cos(\frac{2x+x}{2})=\frac{1}{2}cos(\frac{x}{2})-\frac{1}{2}cos(\frac{3x}{2})$ (b) See graph (red).