Can you help me with trigonometric functions?

Question

Sketch a graph of each function for one period. Label the x-intercepts and any asymptotes. 

 

a) f(x)=sin(x-pie)-1

 

b) f(x)=-3cos[4(x+pie/2)]

Answer 1

Every trigonometry textbook has chapter(s) dealing with transformations of the basic graphs of sine & cosine.  They are worthy of careful study.

 

For example, for a) y = sin(x-pi)-1, two things occur:

1.  the graph of y = sin x is shifted so that it begins not at (0,0) but at (pi,0)...this is a horizontal translation pi units to the right.

2. every y value is reduced by 1; the effect is to lower the entire graph one unit (vertical shift, downward). 

In this instance, the period of the sine graph is not changed, nor is its amplitude.

 

For b) f(x)=-3cos[4(x+pi/2)] there are several changes. You can set the argument [4(x+pi/2)] to 0 and to 2pi, and get the information about the beginning & ending of one cycle (period). This reveals the phase shift. After graphing the compressed & relocated cosine, all the y-values are multiplied by -3 (3 being amplitude) so that the graph is reflected in the x-axis.

 

You may find that using a graphing calculator is an effective aid in visualization. Google topics such as 'transformation of sine graphs' too.