F(x)=cos2x and g(x) =-sin x. Sketch the graphs of f and g on the same set es (-90,90)
I can not do much for you. just take some values of x like - 90,-60, - 45, -30, 0 , 30, 45 etc and do your graphs
Excellent graphing help can be had at
http://rechneronline.de/function-graphs/
For your example, I'd enter two functions:
cos(2x*pi/180)
-sin(x*pi/180)
and set the x range from -100 to 100
and set the y range from -1 to 1
The pi/180 factor is needed because it plots the angle in radians, not degrees.
To sketch the graphs of f(x) = cos(2x) and g(x) = -sin(x) on the same set of axes, you need to follow these steps:
1. Determine the key characteristics of the graphs:
- The function f(x) = cos(2x) is a cosine function with a period of 2π/2 = π.
- The function g(x) = -sin(x) is a sine function with a period of 2π.
2. Determine the range of x-values that you want to plot, which in this case is (-90, 90).
3. Select a suitable grid and label the x-axis and y-axis accordingly. Since the range of x-values is only (-90, 90), you can select an interval of 30 degrees for the x-axis grid.
4. Plot the points on the graph for both functions:
- For f(x) = cos(2x), choose a few values of x within the range (-90, 90), and calculate the corresponding y-values using the cosine function. Plot these points on the graph.
- For g(x) = -sin(x), choose a few values of x within the range (-90, 90), and calculate the corresponding y-values using the sine function. Plot these points on the graph.
5. Connect the plotted points to create a smooth curve for each function:
- For f(x) = cos(2x), connect the plotted points with a smooth curve that oscillates between 1 and -1 every π/2 units.
- For g(x) = -sin(x), connect the plotted points with a smooth curve that oscillates between -1 and 1 every π/2 units.
6. Label the functions on the graph:
- Label the graph of f(x) as "f(x) = cos(2x)."
- Label the graph of g(x) as "g(x) = -sin(x)."
By following these steps, you should be able to sketch the graphs of f(x) = cos(2x) and g(x) = -sin(x) on the same set of axes.