what does the (3x - π) mean in a cosine graph?

Question

equation: y = 2 cos(3x - π) on the interval -2π ≤ x ≤ 2π

i know...
-the "2" is the amplitude, which means the graph starts at unit 2 on the graph.
-the "-π" means the graph would move to the right

but the rest, i'm unsure. thanks for the help.

Answer 1

3 is the frequency. So if cos(x-pi) is period 2pi moved to the right, cos(3x-pi) will have period 2pi/3 and be moved pi to the right.

In general Acos(Bx-C)
A = amplitude
B = frequency => period = 2pi/B
C = phase shift => move to left or right C

Answer 2

The "3x" part means how compressed or streched the graph is horizontally, i.e. how many waves fit within a 360 degree cycle. So in this case the number of waves in 360 is 3 waves, and the cycle repeats itself every 360/n degrees, where n is the number in front of the x.

So...

Cycle repeat = 360/3 degrees

= 120 degrees

Also the - pi, means how far the graph is "shoved", and when dealing with radians, pi = 180 degrees.

So your entire graph would be shoved 180 degrees to the right.


Hope this helps!

Answer 3

set everything in parintheses equal to zero and 2pi to get the greatest and smallest points at which the graph intersects the x-axis. Find the average of those 2 points to find the middle point. Find the average of the middle point and the smallest point to find the second point that it intersects. Find the average of the middle and highest points to find the second highest point. Put these points on the graph, start at 2 on the y-axis, go down to (2nd smallest, 0) to (middle,-2) to (second highest,0) to (higest, 2)

It's not nearly as hard as I make it sound. 3x-pi means that all the points moves to the right pi/3.

Answer 4

y
= 2 cos(3x - π)
= 2 Cos(π - 3x)
= - 2 Cos(3x)

Now just draw the curve in the required interval -2π ≤ x ≤ 2π