a car's flywheel has a timing mark on it's outer edge. the height of the timing mark on the rotating flywheel is given by y=3.55sin[x - (pi/4)]. graph one full cycle of this function.
I was not taught how to graph a function like this, only the simple y= sin x and y= cos x functions. Please help me. you do not have to provide a graph as long as you clearly explain how i would put it on a graph.
as a note: the graph i have has x values of 0 to 2pi and y values of 4 to -4. Thank you and God bless!
y= A sin Theta
you can graph that. Now let A= 3.55
Now let theta= x-PI/4
That means theta is zero when x=PI/4. So it is a sine curve shifted to the right by PI/4
You can plot that.
bobpursely: Thank you so much! God bless you for taking the time to help!
To graph the function y = 3.55sin[x - (π/4)], we can break the process down into a few steps:
1. Determine the x-values: In the given function, it has been mentioned that the x-values range from 0 to 2π. These values represent one full cycle of the function.
2. Calculate the y-values: Use the given function y = 3.55sin[x - (π/4)] to find the corresponding y-values for each x-value in the range specified. Plug in the x-values and evaluate the function to obtain the y-values.
3. Plot the points: Create a set of coordinates using the x and y-values obtained. For example, if the x-value is 0 and the corresponding y-value is 0, the coordinate is (0,0). Similarly, if the x-value is π/2 and the y-value is 3.55, the coordinate is (π/2, 3.55). Plot all the points obtained in this manner.
4. Draw the graph: Once all the points are plotted, connect them to create a smooth curve. Remember that the function is sinusoidal, so the curve will repeat itself after completing one full cycle.
Based on the given information, the y-values range from 4 to -4. To make sure the graph fits within this range, adjust the vertical scale accordingly. Divide the range of y-values (8 units) by the desired range on the graph (8 units as well) to determine the appropriate scale.
For example, you could use a scale where each unit on the vertical axis represents 1 unit on the graph. In this case, you would mark the y-axis at intervals of 1 from 4 to -4.
Remember to label the x and y-axes and indicate any important points, such as the maximum and minimum values.
While I cannot provide a visual graph directly in text form, you can use this explanation to sketch the graph on a piece of paper or input the function into a graphing calculator or software to visualize the graph.