Question

GRAPH 3cosPi(x-1)-1 HELP

Answer 1

cos(x) has a period of 2(pi). That means the graph repeats itself every 2(pi) along the x-axis. cos(A*x) has a period of 2(pi) / A. It will repeat itself every 2(pi) / A along the x axis.

In this problem, 3cosPi(x-1)-1, x is being multiplied by pi. Its period will be 2(pi) / pi = 2.
cos(x) has an amplitude of 1. That means it will go up to +1 along the positive y axis and -1 along the negative y axis.

Bcos(x) will have have an amplitude of B. It will go from -B to + B.

In this problem, cos is being multiplied by 3. So the graph should go from -3 to + 3 along the y axis.

Answer 2

If you graph cos(x) and cos(x-1), the second graph will simply be cos(x) shifted to the right by 1 unit. Anytime you replace x by x-a you will be shifting the graph by "a" units to the right. Here, 3cosPi(x-1)-1 = 3cos((pi)x - pi) - 1
We are subtracting pi which means the graph will shift to the right by pi units.

And finally, we are subtracting 1. That means the graph is being shifted down by 1 unit.

You can start with a cos(x) graph (without actually plotting it) and use the above information to graph 3cos((pi)x - pi) - 1.

This long method is to understand translation, dilation, etc.

But if you want a short method, simply put in some values for x, calculate the corresponding values for y and just plot those points.

Answer 3

Yeah I wanted to make a table of values, but pi messed me up. could you show me how I would make the table?

Answer 4

The period for this function is 2. So if you go from x = 0 to x = 2 that will complete one full cycle in the positive x direction. Then you can repeat the graph both in the negative x direction and in positive x direction past x = 2.

Set your calculator to radians. y = 3cosPi(x-1)-1. Try to create a table with x = 0.1, 0.2, 0.3, et.c until x reaches 2. That will be 20 plot points. If you want less, increase x in steps of 0.2 and create a table and you will have only 10 points.

Answer 5

oh okay thank you. So whatever the period is, just sub in any values between 0.-2? after subbing that in, it'll give me my ys and I just plot the graph ?

Answer 6

I dont have to do anything with degrees?

Answer 7

No.

Answer 8

thanks

Answer 9

you are welcome.