Basic Technical Mathematics, 11th Edition

10.6 Composite Trigonometric Curves

• Additional of Ordinates • Parametric Equations • Lissajous Figures

Many applications involve functions that in themselves are a combination of two or more simpler functions. In this section, we discuss methods by which the curve of such a function can be found by combining values from the simpler functions.

EXAMPLE 1 Function that is sum of simpler functions

Sketch the graph of $y\hspace{0.17em}=\hspace{0.17em}2\hspace{0.17em}+\hspace{0.17em}\sin 2x\hspace{0.17em}.\hspace{0.17em}$

This function is the sum of the simpler functions $y_1\hspace{0.17em}=\hspace{0.17em}2$ and $y_2\hspace{0.17em}=\hspace{0.17em}\sin 2x\hspace{0.17em}.\hspace{0.17em}$ We may find values for y by adding 2 to each important value of $y_2\hspace{0.17em}=\hspace{0.17em}\sin 2x\hspace{0.17em}.\hspace{0.17em}$

For $y_2\hspace{0.17em}=\hspace{0.17em}\sin 2x\hspace{0.17em},\hspace{0.17em}$ the amplitude is 1, and the period is $2\pi \hspace{0.17em}/\hspace{0.17em}2\hspace{0.17em}=\hspace{0.17em}\pi \hspace{0.17em}.\hspace{0.17em}$ Therefore, we obtain the values in the following table and sketch the graph in Fig. 10.38 ...