(3) When the graph of a sinusoidal function involves both horizontalscaling and horizontal shifting there are two possibilities:y = sin (m(x – k)) andsin (mx – k')).In words: we can doing the shifting first and then the scaling,or vice versa. Note that if these graphs are to be the same wemust have k = mk.!!In one of these the shift amount is the actual distance thegraph is shifted. In the other the shift amount is known as aphase angle - it gives the shift as a fraction of a full rotation.Have each member of your group create a graphthe samegraph!in both forms. In other words everybody choose arandom horizontal scaling factor and a random shift amountand plot it in the two forms above. Discuss the evidence youobtain and determine which form is the phase angle version andwhich is the true horizontal shift version.

The general form of a sinusoidal curve is given by: y=AsinBx-C+D For the given question we have…

(3) When the graph of a sinusoidal function involves both horizontal scaling and horizontal shifting there are two possibilities: sin (m(x – k)) and y = sin (mr – k')). - In words: we can doing the shifting first and then the scaling, or vice versa. Note that if these graphs are to be the same we must have k' = mk.

(3) When the graph of a sinusoidal function involves both horizontal scaling and horizontal shifting there are two possibilities: sin (m(x – k)) and y = sin (mr – k')). - In words: we can doing the shifting first and then the scaling, or vice versa. Note that if these graphs are to be the same we must have k' = mk.

Trigonometry (11th Edition)

11th Edition

ISBN:9780134217437

Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Chapter1: Trigonometric Functions

Section: Chapter Questions

Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.

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Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.

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(3) When the graph of a sinusoidal function involves both horizontal
scaling and horizontal shifting there are two possibilities:
y = sin (m(x – k)) and
sin (mx – k')).
In words: we can doing the shifting first and then the scaling,
or vice versa. Note that if these graphs are to be the same we
must have k = mk.
!!
In one of these the shift amount is the actual distance the
graph is shifted. In the other the shift amount is known as a
phase angle - it gives the shift as a fraction of a full rotation.
Have each member of your group create a graph
the same
graph!
in both forms. In other words everybody choose a
random horizontal scaling factor and a random shift amount
and plot it in the two forms above. Discuss the evidence you
obtain and determine which form is the phase angle version and
which is the true horizontal shift version.

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