Plotting 4sin2xsinx +2 -2cos(4x) + 1/2 - 1/2cos(2x)

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In summary, the conversation discusses rewriting a mathematical formula in order to plot it using Excel. The formula is 4sin^(2) 2x + 4sin2xsinx + sin^(2)x and is rewritten as 4sin2xsinx + 2 -2cos(4x) + 1/2 - 1/2cos(2x). The use of the fact that sin^(2)x = 1/2 - 1/2cos(2x) is also mentioned. The person expressing uncertainty about how to enter sin^(2)x into Excel is reassured that their method looks fine.
  • #1
andrey21
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I have found a magnitude to be the following:

4sin^(2) 2x + 4sin2xsinx + sin^(2)x


I now need to plot this using excel so I have rewritten it as:

4sin2xsinx + 2 -2cos(4x) + 1/2 - 1/2cos(2x)

4sin2xsinx +5/2 - 2cos(4x) -1/2cos(2x)

Using the fact:

sin^(2)x = 1/2 - 1/2cos(2x)

Is this correct?
 
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  • #2
What you did looks fine, but how does it help? Why not just plug the original formula into Excel to plot it?
 
  • #3
I was just a little unsure how to enter sin^2... in Excel. But aslong as other way looks fine i don't mind using that formula. Thanks Vela
 

1. What is the purpose of plotting the equation 4sin2xsinx +2 -2cos(4x) + 1/2 - 1/2cos(2x)?

The purpose of plotting this equation is to visualize the behavior and relationship between the different trigonometric functions and constants involved. It can also help in identifying key features such as the amplitude, period, and phase shift.

2. How do you plot this equation on a graph?

To plot this equation, you will first need to determine the range of values for the independent variable, x. Then, use a calculator or mathematical software to evaluate the equation for various values of x. Finally, plot the resulting points on a graph and connect them to create a smooth curve.

3. What are the main components of this equation?

The main components of this equation are the trigonometric functions (sine and cosine), constants (4, 2, 1/2), and the independent variable, x. Each of these components plays a role in determining the overall shape and behavior of the plotted curve.

4. How does the value of the constants affect the graph?

The value of the constants in this equation can affect the amplitude, period, and phase shift of the graph. For example, a larger value for the constant 4 will result in a larger amplitude, while a smaller value for the constant 1/2 will result in a smaller amplitude.

5. What are some key features to look for when analyzing the graph of this equation?

Some key features to look for when analyzing the graph of this equation include the amplitude, period, phase shift, and any intersections with the x-axis. Additionally, you can also identify any local maximum or minimum points, as well as the overall trend of the graph (increasing or decreasing).

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