This applet helps you explore the general cosine function
f(x) = a*cos(bx + c) + d
and its properties such as amplitude, period and phase shift
by changing the parameters a, b, c and d. Particular exloration of the phase shift is undertaken by plotting
f(x) = a*cos(bx + c) + d
in blue and
f(x) = a*cos(bx) + d
in red as shown in the figure below. This is to explain the effects of c on the phase shift.
You may also want to consider another tutorial on the trigonometric unit circle .
Once you finish the present tutorial, you may want to go through a self test on trigonometric graphs .
Two possibilities to explore graph of functions of the form f(x) = a*cos(bx + c) + d
1) Using a cosine Function HTML5 applet
2) Using a Java applet
Click on the button above "click here to start" and maximize the window obtained.
Explore how the 4 coefficients a,b,c and d affect the graph of f(x)?
Links to topics related to cosine function
Use the scrollbar to set a=1,b=1,c=0 and d=0. Write down f(x) and take note of the amplitude, period and phase shift of f(x)? Now change a , how does it affect the graph?
Set a=1,c=0,d=0 and change b. Find the period from the graph and compare it to 2pi/|b|. How does b affect the graph of f(x)?
set a=1,b=1,d=0 and change c starting from zero going slowly to positive large values. Take note of the shift, is it left or right, and compare it to
set a=1,b=1,d=0 and change c starting from zero going slowly to negative smaller values. Take note of the shift, is it left or right, and compare it to
repeat 3 and 4 above for b=2,3 and 4.
set a,b and c to non zero values and change d. What is the direction of the shift of the graph when d is positive and when d is negative?
Step by Step Math Worksheets SolversNew !
Linear ProgrammingNew !
Online Step by Step Calculus Calculators and SolversNew !
Factor Quadratic Expressions - Step by Step CalculatorNew !
Step by Step Calculator to Find Domain of a Function New !
Free Trigonometry Questions with Answers
Interactive HTML5 Math Web Apps for Mobile LearningNew !
Free Online Graph Plotter for All Devices
Home Page --
HTML5 Math Applets for Mobile Learning --
Math Formulas for Mobile Learning --
Algebra Questions -- Math Worksheets
Free Compass Math tests Practice
Free Practice for SAT, ACT Math tests
Precalculus Tutorials --
Precalculus Questions and Problems
Precalculus Applets --
Equations, Systems and Inequalities
Online Calculators --
Geometry Tutorials --
Geometry Calculators --
Calculus Tutorials --
Calculus Questions --
Applied Math --
Math Software --
High School Math --
Middle School Math --
Math Videos From Analyzemath
Updated: February 2015
Copyright © 2003 - 2016 - All rights reserved
More To Explore