How to plot the graph of #f(x)=cos 8(pi)#?

Question

Carter Anderson · Accepted Answer

The line #y = 1#.

First of all, note that there is no dependence of the function on #x#. Thus it is a constant function. We need to find the value of the function. We know that the period of #cos# is #2pi#. Thus we write: # cos(8pi) = cos(0 + 4 . 2pi) = cos(0) = 1 # Thus the graph of the function is #y = 1#, a line parallel to the x-axis having y-intercept of 1.

Oliver Atkinson · Answer

undefined To plot the graph of $ f(x) = \cos(8\pi) $, follow these steps:

1. Understand the function: The function $ f(x) = \cos(8\pi) $ represents the cosine function evaluated at $ x = 8\pi $. The cosine function oscillates between -1 and 1 as $ x $ varies.

2. Determine the value of $ \cos(8\pi) $: Since the cosine function has a period of $ 2\pi $, $ \cos(8\pi) $ evaluates to the same value as $ \cos(0) $ because $ 8\pi $ is a multiple of $ 2\pi $. Therefore, $ \cos(8\pi) = \cos(0) = 1 $.

3. Plot the point: At $ x = 8\pi $, the value of the function $ f(x) $ is 1. Plot the point (8π, 1) on the coordinate plane.

4. Draw the graph: Since $ \cos(8\pi) = 1 $ and the cosine function repeats every $ 2\pi $ units, the graph of $ f(x) = \cos(8\pi) $ is a horizontal line passing through the point (8π, 1) on the coordinate plane.

5. Optional: If you want to show more of the cosine function's behavior, you can extend the graph in both directions along the x-axis, with the same horizontal line repeating every $ 2\pi $ units.

Therefore, to plot the graph of $ f(x) = \cos(8\pi) $, you draw a horizontal line passing through the point (8π, 1) on the coordinate plane.