# Cosine Function

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 . Interactive Tutorials 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 Your browser is completely ignoring the tag! 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)? 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 -c/b. 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 -c/b. 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? Links to topics related to cosine function