Graphing Cos(x) | Understanding the Periodic Nature of the Cosine Function

Graph of cos(x)

The graph of cos(x) is a periodic function that represents the cosine of an angle x

The graph of cos(x) is a periodic function that represents the cosine of an angle x.

To graph cos(x), you will need to plot several points on the coordinate plane and then connect them to form a curve.

First, let’s consider the domain and range of cos(x). The domain of cos(x) is all real numbers since the cosine function is defined for any angle. The range of cos(x) is between -1 and 1, inclusive.

To plot the graph, you can start by selecting some key points that lie on the curve. These points will help you determine the shape and characteristics of the graph.

1. At x = 0, cos(0) = 1. So, plot the point (0, 1) on the coordinate plane.
2. At x = π/2, cos(π/2) = 0. Plot the point (π/2, 0).
3. At x = π, cos(π) = -1. Plot the point (π, -1).
4. At x = 3π/2, cos(3π/2) = 0. Plot the point (3π/2, 0).
5. At x = 2π, cos(2π) = 1. Add the point (2π, 1) to your graph.

To complete the graph, notice that cos(x) is a periodic function with a period of 2π. This means that the graph repeats itself every 2π units of x.

So, you can continue plotting points that are 2π units away from the ones you have already plotted. For example:
– At x = 4π, cos(4π) = 1.
– At x = 5π/2, cos(5π/2) = 0.
– At x = 3π, cos(3π) = -1.

You can continue this pattern and plot as many points as you need to see the full graph.

Next, connect the plotted points with a smooth curve. The graph of cos(x) is a symmetrical wave-like curve with a maximum value of 1 and a minimum value of -1. It oscillates between these extremes as x increases.

Remember to label the x and y axes of the graph. The x-axis represents the angle measurement, while the y-axis represents the value of cos(x).

The final graph should have a wave-like shape, passing through the points you plotted, and repeating every 2π units.

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