Solve & plot a graph for the following: F(X)=cos(X)-cos to second power X for the interval negative pi greater than or equal to X less than or equal to positive pi
To solve and plot the graph of the function f(x) = cos(x) - cos^2(x) for the interval -π ≤ x ≤ π, we can follow these steps:
Step 1: Determine the values of f(x) for different values of x within the given interval.
Step 2: Plot the points (x, f(x)) on a graph.
Step 3: Connect the plotted points to obtain the graph of the function.
Let's begin by calculating the values of f(x) for various x within the interval -π to π. We'll use increments of π/10 for convenience:
For x = -π:
f(-π) = cos(-π) - cos^2(-π) = -1 - (-1)^2 = -1 - 1 = -2
For x = -9π/10:
f(-9π/10) = cos(-9π/10) - cos^2(-9π/10)
Continue this process until we obtain values for each x within the given interval.
Once we have computed the values, we can plot them on a graph. The x-axis will represent the values of x in the interval -π ≤ x ≤ π, while the y-axis will represent the corresponding values of f(x). Connect the plotted points to create the graph.