Some graphing calculator models include an integrated computer algebra system (CAS) for performing symbolic calculations. A symbolic approach to problem solving can be much more informative than a numerical approach. The following steps apply specifically to HP graphing calculator models with CAS, but the same general approach applies almost universally.
Instructions
1. Hit the "CAS" button in the home view of the graphing calculator to enter the CAS environment. The menus for CAS appear on the bottom of the screen and offer a range of functions and adjustable parameters.
2. Configure the CAS settings. Depending on the type of problem you're solving, you may need to set the parameters carefully. Alternatively, if you want just the basic default settings, configure the settings to default using the "ALGB" menu and the "CFG" option.
3. Enter the equation or expression that you want to manipulate or solve. If you're working with a single variable, you can just use the "X, T, Theta" button to quickly enter the variable. Otherwise, use the "ALPHA" button to enter a different variable. You can use the arrow buttons for highlighting expressions.
4. Highlight the expression or equation when you're ready to perform a manipulation or to get a solution. Use the menus at the bottom of the screen to choose the operation, whether it be factoring, differentiation, integration, solution or another type of operation. You can also simply hit "ENTER" to perform an evaluation.
5. Reformat the solution if necessary. The result may not be in the format you want, so you may need to expand it, for example. Simply go back to Step 4 to do this.
Tips & Warnings
- The owner's manual is the best reference for the details concerning all the different possible uses of a graphing calculator CAS. Different manufacturers may have different syntaxes or procedures for using the CAS on their graphing calculator models.
- Experimentation is the best way to learn how to use the CAS feature on a graphing calculator. The more time you spend with it, the more familiar you'll become.
Friday, August 9, 2013
Display a Graph on a Calculator
Displaying a mathematical graph requires a special device called a graphing calculator. Users input math functions into the calculator and then it plots those functions on a grid. Displaying a graph on a calculator often helps understand how a function appears in the physical world. It only takes a few minutes to set up a graph display. Different calculators used different terms for the relevant functions, but work in basically the same way.
Instructions
1. Turn on the graphing calculator by pressing the "Power" button, which will most likely be labeled "On." Check your graphing calculator's manual for the specific location of the power button.
2. Navigate to the graph plotting menu. The graph menu button can be called different names in different calculators. For example, in the Casio FX-9750 graphing calculator, you reach the menu by pressing the "Graph" button. Enter the mathematical function you wish to graph with the numbered buttons. The function must include a variable letter like "X" to graph properly. Press the "X" button to enter the "X" variable into your function. Review your graphing calculator's user manual for information on creating more complex functions.
3. Press the "Graph" button and view the new graph. In the TI 83 calculators you should press the "Graph" button while in the Casio FX-9750 you should press the "Draw" button. The calculator will automatically display the mathematical function as a graph.
4. Re-size the graph window to display the image more clearly. Your graph will likely either appear too small on the calculator or too large. If the graph looks too small you should zoom in on the image. You can do this on the TI-83 graphing calculator by pressing the "Zoom" button. The button may be called something different on your specific calculator however. Continue pressing the button to make the image larger. If the image you graph looks too large you should zoom out. You can do this on Casio FX-9750 by pressing the "F4" button. Continue to use the "Zoom Out" button until you like appearance of the graph.
Instructions
1. Turn on the graphing calculator by pressing the "Power" button, which will most likely be labeled "On." Check your graphing calculator's manual for the specific location of the power button.
2. Navigate to the graph plotting menu. The graph menu button can be called different names in different calculators. For example, in the Casio FX-9750 graphing calculator, you reach the menu by pressing the "Graph" button. Enter the mathematical function you wish to graph with the numbered buttons. The function must include a variable letter like "X" to graph properly. Press the "X" button to enter the "X" variable into your function. Review your graphing calculator's user manual for information on creating more complex functions.
3. Press the "Graph" button and view the new graph. In the TI 83 calculators you should press the "Graph" button while in the Casio FX-9750 you should press the "Draw" button. The calculator will automatically display the mathematical function as a graph.
4. Re-size the graph window to display the image more clearly. Your graph will likely either appear too small on the calculator or too large. If the graph looks too small you should zoom in on the image. You can do this on the TI-83 graphing calculator by pressing the "Zoom" button. The button may be called something different on your specific calculator however. Continue pressing the button to make the image larger. If the image you graph looks too large you should zoom out. You can do this on Casio FX-9750 by pressing the "F4" button. Continue to use the "Zoom Out" button until you like appearance of the graph.
Find the Cotangent on a Graphing Calculator
In trigonometry, the cotangent is the reciprocal of the tangent. The formula for determining the tangent is the opposite side divided by the adjacent side of a triangle. So, since the cotangent is the reciprocal, then the formula for determining the cotangent is the adjacent side divided by the opposite side of the triangle. When inputting cotangent into a graphing calculator, you need to know the angle in degrees for which you are trying to find the cotangent.
Instructions
1. Type "1" into your graphing calculator.
2. Press the division sign. The calculator is now prepared to perform a reciprocal calculation.
3. Press the button marked "TAN."
4. Type the angle for which you are calculating the cotangent.
5. Press "ENTER" to solve for the cotangent.
Instructions
1. Type "1" into your graphing calculator.
2. Press the division sign. The calculator is now prepared to perform a reciprocal calculation.
3. Press the button marked "TAN."
4. Type the angle for which you are calculating the cotangent.
5. Press "ENTER" to solve for the cotangent.
Using a Graphing Calculator to Calculate an Arc Length
Math and science students use graphing calculators to plot two-dimensional graphs of functions, solve equations, and calculate derivatives and integrals. In calculus, you can find the arc length of a curve by evaluating an integral related to the curve's equation. A graphing calculator can evaluate the integral in less than a second, whereas by hand it may take several minutes depending on the complexity of the function.
Instructions
1. Write down the derivative of the function whose arc length you want to compute. For example, suppose you are calculating the arc length of f(x) = e^(2x) over a finite interval. The derivative of this function is f ' (x) = 2e^(2x).
2. Open the integral evaluation screen on your graphing calculator. On Texas Instruments devices, do this by hitting the "MATH" button, choosing the "Math" menu and then selecting "fnInt" from the drop down submenu.
3. Enter the function sqrt(1 + (f ' (x))^2) on the screen and enter a comma at the end of the function. Replace "f ' (x)" with the derivative of the function you are working on. The expression sqrt(1 + (f ' (x))^2) is the formula for the arc length of a function f(x). For instance, if f(x) = e^(2x) and f ' (x) = 2e^(2x) then you enter sqrt(1 + (2e^(2x))^2) followed by a comma.
4. Enter "x" followed by a comma. You must do this so the calculator knows what the variable is.
5. Enter the lower endpoint of the arc's interval, followed by a comma. For instance, if you are evaluating the arc length over the interval from 3 to 4, you enter 3 followed by a comma.
6. Enter the upper endpoint of arc's interval followed by a closing parenthesis. For instance, if 4 is the upper endpoint, you enter 4).
7. Hit the enter key to evaluate the integral. The length of the arc will appear below the commands you entered.
Instructions
1. Write down the derivative of the function whose arc length you want to compute. For example, suppose you are calculating the arc length of f(x) = e^(2x) over a finite interval. The derivative of this function is f ' (x) = 2e^(2x).
2. Open the integral evaluation screen on your graphing calculator. On Texas Instruments devices, do this by hitting the "MATH" button, choosing the "Math" menu and then selecting "fnInt" from the drop down submenu.
3. Enter the function sqrt(1 + (f ' (x))^2) on the screen and enter a comma at the end of the function. Replace "f ' (x)" with the derivative of the function you are working on. The expression sqrt(1 + (f ' (x))^2) is the formula for the arc length of a function f(x). For instance, if f(x) = e^(2x) and f ' (x) = 2e^(2x) then you enter sqrt(1 + (2e^(2x))^2) followed by a comma.
4. Enter "x" followed by a comma. You must do this so the calculator knows what the variable is.
5. Enter the lower endpoint of the arc's interval, followed by a comma. For instance, if you are evaluating the arc length over the interval from 3 to 4, you enter 3 followed by a comma.
6. Enter the upper endpoint of arc's interval followed by a closing parenthesis. For instance, if 4 is the upper endpoint, you enter 4).
7. Hit the enter key to evaluate the integral. The length of the arc will appear below the commands you entered.
Calculate the Z-Score Area on a Graphing Calculator
A Z-score is a statistical tool that describes how many standard deviations a data point lies from the average in a given set of data. The Z-score may also be called the standard score, Z-value, normal score or the standardized variable. Calculating a Z-score by hand is a long and difficult process. Luckily, graphing calculators provide a quick way to calculate the Z-score.
Instructions
1. Determine the area "p" for which you would like to calculate the z-score. "P" represents the percentage of data that lies below the Z-score. For example, if you choose p = 70 percent and calculate a Z-score of 0.8, you can say that 70 percent of your data lies within 0.8 standard deviations from the mean.
2. Press the "2nd" key on your graphing calculator. You will notice that every key on your calculator has large text on the button (the primary menu) and smaller text above the button (the secondary menu). By pressing this key, you activate the secondary menu.
3. Press the "VARS" key, which has the secondary "DISTR" menu printed above it. Your screen will display the distribution menu.
4. Click the down arrow to select "3: invNorm(" on the menu. Press "Enter."
5. Type the "p" value that you determined in Step 1 as a decimal. For example, if you decided on p = 70 percent, type 0.7. Press "Enter." The graphing calculator will return the Z-value.
Instructions
1. Determine the area "p" for which you would like to calculate the z-score. "P" represents the percentage of data that lies below the Z-score. For example, if you choose p = 70 percent and calculate a Z-score of 0.8, you can say that 70 percent of your data lies within 0.8 standard deviations from the mean.
2. Press the "2nd" key on your graphing calculator. You will notice that every key on your calculator has large text on the button (the primary menu) and smaller text above the button (the secondary menu). By pressing this key, you activate the secondary menu.
3. Press the "VARS" key, which has the secondary "DISTR" menu printed above it. Your screen will display the distribution menu.
4. Click the down arrow to select "3: invNorm(" on the menu. Press "Enter."
5. Type the "p" value that you determined in Step 1 as a decimal. For example, if you decided on p = 70 percent, type 0.7. Press "Enter." The graphing calculator will return the Z-value.
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