To solve the equation 7cos(2t) = 3 in the interval from 0 to 2π, follow these steps:
1. Enter the equation into the graphing calculator: Press the "Y=" button and enter "7cos(2x)=3".
2. Set the viewing window: Press the "WINDOW" button and set the Xmin to 0, Xmax to 2π, Ymin to -7, and Ymax to 7. Press "GRAPH" to see the graph.
3. Find the intersection points: Press the "2ND" button and then the "TRACE" button. Select "Intersect" and press "ENTER". Move the cursor to the left of the first intersection point and press "ENTER". Move the cursor to the right of the first intersection point and press "ENTER". Repeat this process to find the second intersection point. The calculator should display the x-coordinate of each intersection point.
4. Round to the nearest hundredth: Write down the x-coordinates of the intersection points and round each one to the nearest hundredth. For example, if the calculator displays an intersection point of x=1.234567, round it to x=1.23.
Therefore, the solutions to the equation 7cos(2t) = 3 in the interval from 0 to 2π are approximately t=0.79 and t=5.50 (rounded to the nearest hundredth).
Show your steps. Use a graphing calculator to solve the equation in the interval from 0 to 2π. Round to the nearest hundredth.
7cos(2t) = 3
3 answers
AAAaannndd the bot gets it wrong yet again!
If it were 7cos(t) = 3 there would be two solutions.
Since it is 7cos(2t) = 3 there will be four solutions:
cos(2t) = 3/7
2t = 1.1278+2kπ or 2π-1.1278 = 5.1553+2kπ
so t = 0.5639, 3.7055 or 2.5776, 5.7192
If it were 7cos(t) = 3 there would be two solutions.
Since it is 7cos(2t) = 3 there will be four solutions:
cos(2t) = 3/7
2t = 1.1278+2kπ or 2π-1.1278 = 5.1553+2kπ
so t = 0.5639, 3.7055 or 2.5776, 5.7192
My apologies for the mistake in my previous answer. You are correct that the equation 7cos(2t) = 3 has four solutions in the interval from 0 to 2π. Here are the correct steps to solve the equation using a graphing calculator:
1. Enter the equation into the graphing calculator: Press the "Y=" button and enter "7cos(2x)=3".
2. Set the viewing window: Press the "WINDOW" button and set the Xmin to 0, Xmax to 2π, Ymin to -7, and Ymax to 7. Press "GRAPH" to see the graph.
3. Find the intersection points: Press the "2ND" button and then the "TRACE" button. Select "Intersect" and press "ENTER". Move the cursor to the left of the first intersection point and press "ENTER". Move the cursor to the right of the first intersection point and press "ENTER". Repeat this process to find all four intersection points. The calculator should display the x-coordinate of each intersection point.
4. Round to the nearest hundredth: Write down the x-coordinates of the intersection points and round each one to the nearest hundredth.
Therefore, the solutions to the equation 7cos(2t) = 3 in the interval from 0 to 2π are approximately t=0.56, t=2.58, t=3.71, and t=5.72 (rounded to the nearest hundredth).
1. Enter the equation into the graphing calculator: Press the "Y=" button and enter "7cos(2x)=3".
2. Set the viewing window: Press the "WINDOW" button and set the Xmin to 0, Xmax to 2π, Ymin to -7, and Ymax to 7. Press "GRAPH" to see the graph.
3. Find the intersection points: Press the "2ND" button and then the "TRACE" button. Select "Intersect" and press "ENTER". Move the cursor to the left of the first intersection point and press "ENTER". Move the cursor to the right of the first intersection point and press "ENTER". Repeat this process to find all four intersection points. The calculator should display the x-coordinate of each intersection point.
4. Round to the nearest hundredth: Write down the x-coordinates of the intersection points and round each one to the nearest hundredth.
Therefore, the solutions to the equation 7cos(2t) = 3 in the interval from 0 to 2π are approximately t=0.56, t=2.58, t=3.71, and t=5.72 (rounded to the nearest hundredth).
3 answers