Use a graphing calculator to solve the equation in the interval from 0 to 2 π. Round to the nearest hundredth.
7 cos (2t) = 3
Using a graphing calculator, follow these steps to solve the equation:
1. Press the "mode" button and make sure the calculator is in "radian" mode.
2. Press the "y=" button and enter the equation 7cos(2x)-3.
3. Press the "zoom" button and select "Zoom Standard" to view the entire graph.
4. Press the "2nd" button and then "trace" button to access the "Calculate" menu.
5. Select "zero" to find the zeros of the function.
6. Move the cursor close to the first zero and press "enter" to calculate it.
7. Move the cursor close to the second zero and press "enter" to calculate it.
8. Round the zeros to the nearest hundredth.
9. The solutions in the interval from 0 to 2π are:
t ≈ 0.74 and t ≈ 2.40
Therefore, the solutions to the equation 7cos(2t) = 3 in the interval from 0 to 2π are approximately t = 0.74 and t = 2.40.
To solve the equation 7 cos(2t) = 3, we can use a graphing calculator to find the values of t within the interval from 0 to 2π (0 ≤ t ≤ 2π) that satisfy the equation.
Here are the steps to solve it using a graphing calculator:
1. Turn on the graphing calculator and enter the equation: "7cos(2x) = 3".
2. Set the calculator to the degree mode (if it's not already in degree mode) since the trigonometric functions are commonly used in degrees.
3. Set the viewing window for t from 0 to 2π.
4. Plot the graph of the equation.
5. Use the calculator's "zero" or "root" feature to find the x-intercepts of the graph, which represent the values of t that satisfy the equation.
6. The calculator will display the solutions for t. Round them to the nearest hundredth.
By following these steps, you will be able to use the graphing calculator to find the values of t that satisfy the equation 7 cos(2t) = 3 within the interval from 0 to 2π.
To solve the equation 7cos(2t) = 3 in the interval from 0 to 2π using a graphing calculator, follow these steps:
1. Turn on your graphing calculator and select the appropriate mode for trigonometric functions (radians).
2. Enter the equation into the calculator by typing "7*cos(2*t) = 3". Make sure to use the asterisk (*) for multiplication and "t" as the variable.
3. Set the viewing window to display the interval from 0 to 2π. To do this, go to the window settings and set the Xmin value to 0 and the Xmax value to 2π.
4. Graph the equation on the calculator by either pressing the "Graph" button or a similar key.
5. Examine the graph to find the x-values where the graph intersects the line y = 3. These will be the solutions to the equation.
6. Use the calculator's trace function or cursor to move along the graph and find the x-values of the intersection points with y = 3.
7. Round the x-coordinates of the intersection points to the nearest hundredth. These rounded values will be the solutions to the equation in the interval from 0 to 2π.
By following these steps, you should be able to use a graphing calculator to find the solutions to the equation 7cos(2t) = 3 in the specified interval.