How do I find the x-intercept of the graph of y=3sin 2x? Could you explain the steps to put this into my graphing calculator to get the graph. Please and thanks
To find the x-intercept of the graph of y = 3sin(2x), we need to determine the values of x where the graph crosses the x-axis.
Step 1: Set y = 0
When the graph crosses the x-axis, the value of y is 0. So, we will replace y with 0 in the equation:
0 = 3sin(2x)
Step 2: Solve for x
To solve for x, we need to isolate it. Divide both sides of the equation by 3:
0/3 = (3sin(2x))/3
0 = sin(2x)
Step 3: Find the angle whose sine is 0
Since you're using a graphing calculator, you can use the SIN function to find the angles for which the sine value is 0. Typically, you would enter SIN^-1(0) on your calculator. However, since we have 2x as the argument, we need to solve:
2x = SIN^-1(0)
Step 4: Determine the solutions
In the interval [0, 2Ο], the sine function is equal to 0 at two points: 0 and Ο. So, we have:
2x = 0 --> x = 0
2x = Ο --> x = Ο/2
These are the x-values where the graph crosses the x-axis, so they represent the x-intercepts.
To graph this equation on your calculator, follow these steps:
1. Turn on your graphing calculator.
2. Enter the equation: y = 3sin(2x).
3. Access the graph menu on your calculator.
4. Set the window or range of x-values you would like to display.
5. Choose the graphing mode (e.g., "Function" or "Y=" mode).
6. Press the graph button to plot the graph of y = 3sin(2x).
7. The x-intercepts appear as the points where the graph crosses the x-axis. Make sure your calculator is set to "Trace" or "Zoom out" to see them clearly.
Remember to consult your calculator's manual or online resources for specific instructions based on your calculator model.