Precalculus with Trigonometry: Concepts and Applications

Paul A. Foerster

Chapter 5 Properties of Combined Sinusoids - all with Video Answers

Educators

Section 1

Introduction to Combinations of Sinusoids

00:42

Problem 1

Plot the graphs of $y_{1}=3 \cos \theta, y_{2}=4 \sin \theta$ and $y_{3}=y_{1}+y_{2}$ on the same screen. Do your graphs agree with the ones in Figure $5-1$ a?

Ankit Gupta

Numerade Educator

01:03

Problem 2

The $y$ a graph in Problem 1 seems to be a sinusoid. Estimate graphically its period, amplitude, and phase displacement (for $y=\cos x)$.

Ankit Gupta

Numerade Educator

01:27

Problem 3

Find numerically the amplitude and phase displacement of $y_{3}$ by using the MAX feature of your grapher to find the first high point. Do the results confirm your estimates in Problem $2 ?$

Adnan Gill

Numerade Educator

03:41

Plot the sinusoid $y_{4}=A \cos (\theta-D),$ where $A$ and $D$ are the amplitude and phase displacement you found numerically in Problem $3 .$ Use a different style for this graph so you can distinguish it from the graph of $y_{3}$ Does the $y$ s graph really seem to be a sinusoid?

Paul Olszewski

Numerade Educator

02:37

Problem 5

Make a table of values of $y_{3}$ and $y_{4}$ for various values of $\theta$. Do the values confirm or refute the conjecture that $y_{3}$ is a sinusoid?