Generally, in lower-level mathematics classes, basic scientific calculators are used in order to speed up simple calculations of addition, subtraction, multiplication and division. As one approaches the study of calculus, however, graphing becomes trivial, just as simple operations were trivial in algebra. This is because in calculus and pre-calculus, there are several other difficult calculations that, when combined with graphing by hand, would add up to an unreasonable amount of time necessary to solve a single problem. It is for this reason that general knowledge of how to use a graphing calculator is valuable and helpful in saving time.
Instructions
1. Prepare the given equation(s) for graphing. Since the TI-83 only naturally graphs equations of the form "Y=", all equations must first be written with an isolated "y" variable before they can be graphed.
2. Turn on the calculator and press the "Y=" button, located right below the screen on the left, in order to enter the graphing interface.
3. Get rid of any past entries in the graphing log by hovering over each occupied line with the cursor and pressing "Clear."
4. Type in each equation of the form "Y=" in separate lines, beginning with line Y1 and continuing downward.
5. Press the "Graph" button (also below the screen, on the right side of the calculator), and wait for the graphs to appear on the XY-plane.
6. Copy the graph on paper if necessary and solve the problem by hand, or, if allowed, press "2nd-Trace" to calculate on the calculator itself. Remember that the graph displayed has a domain of {-10,10} and a range of {-10,10} when copying it onto paper.
Tips & Warnings
- Use parentheses liberally when entering an equation. When dealing with fractions, for example, it is best to enclose both the numerator and denominator in parentheses.
- Try zooming in or out of the default graph window by pressing the "Zoom" button and selecting the appropriate sub-option. Some parts of the graph may be invisible in the default window.
- Avoid excessive reliance on your graphing calculator, especially in timed situations. Sometimes it is easier to graph by hand, or skip graphing entirely if the problem does not require it.
Friday, August 9, 2013
Download Games Onto a Graphing Calculator
The first use for graphing calculator is, of course, to graph complex mathematic equations. However, like anything else, it doesn't take much time before there's a temptation to use it for entertainment. There are few high school students that graduate without at least one game on their graphing calculator. For those few, here's how to get them. Since Texas Instruments (TI) is the predominant brand, the instructions revolve around this type.
Instructions
1. Acquire the connectivity software. For most TI calculators, the TIConnect program will work. Visit the Texas Instruments education resources site, provided below, and click the "Downloads" button. Choose the "Apps & Software" option and click "Connectivity Software" under the "Computer Software" heading. Choose the correct version from the list and download it to your computer.
2. Run the program to install the software.
3. Download the game program or programs. The safest option is to download them directly from the TI site through the "Games" option in the "Downloads" menu. The next safest option is to download from a site linked on the TI site. The least safe option, but one that may provide the widest variety of options, is to do an Internet search for games for your particular model.
4. Connect your calculator to your computer using the provided cord. If the provided cable is a USB cable, which most are, your computer should detect your calculator as an external device automatically.
5. Open the TIConnect program and click the "TI Device Explorer" button. A window pops up and will try to connect to your calculator. Choose the port your calculator is connected to.
6. Ensure the folder where your game is located is open. Drag and drop the game file from that folder to the Device Explorer pop up Window.
7. Wait until the transfer is complete. Then disconnect your calculator and close the TIConnect program.
Instructions
1. Acquire the connectivity software. For most TI calculators, the TIConnect program will work. Visit the Texas Instruments education resources site, provided below, and click the "Downloads" button. Choose the "Apps & Software" option and click "Connectivity Software" under the "Computer Software" heading. Choose the correct version from the list and download it to your computer.
2. Run the program to install the software.
3. Download the game program or programs. The safest option is to download them directly from the TI site through the "Games" option in the "Downloads" menu. The next safest option is to download from a site linked on the TI site. The least safe option, but one that may provide the widest variety of options, is to do an Internet search for games for your particular model.
4. Connect your calculator to your computer using the provided cord. If the provided cable is a USB cable, which most are, your computer should detect your calculator as an external device automatically.
5. Open the TIConnect program and click the "TI Device Explorer" button. A window pops up and will try to connect to your calculator. Choose the port your calculator is connected to.
6. Ensure the folder where your game is located is open. Drag and drop the game file from that folder to the Device Explorer pop up Window.
7. Wait until the transfer is complete. Then disconnect your calculator and close the TIConnect program.
Plot Line Segments on Graphing Calculator
In Algebra class, a student becomes accustomed to using a graphing calculator to graph lines, functions and line segments. You need to be able to graph all three of these without your calculator, but if you want to quickly visualize a line segment, or a portion of a line defined specifically between two coordinates, your graphing calculator can instantaneously create such a graph.
Instructions
1. Access the "draw" menu, and select the line command. The calculator will display the "Line" function, along with open brackets.
2. Enter the coordinates of the endpoints of the line segment, separated by commas, in the form "Line(X1, Y1, X2, Y2)". If, for instance, the coordinates if your line segment are "(0,3)" and "(1,2)", you would enter "Line(0,3,1,2)".
3. Press "Enter" and your calculator will plot the segment.
Instructions
1. Access the "draw" menu, and select the line command. The calculator will display the "Line" function, along with open brackets.
2. Enter the coordinates of the endpoints of the line segment, separated by commas, in the form "Line(X1, Y1, X2, Y2)". If, for instance, the coordinates if your line segment are "(0,3)" and "(1,2)", you would enter "Line(0,3,1,2)".
3. Press "Enter" and your calculator will plot the segment.
Compound Interest Using a Graphing Calculator
Compound interest is a situation that occurs when interest is added to a balance and then at a later date, interest is added to the original deposit plus the interest that was already calculated. The formula for compound interest is A = P*(1 + (r/n))^(n*t) where A is the total amount after the interest is compounded, P is the principal amount, r is the annual interest rate as a decimal, t is the number of years and n is the number of times interest is compounded per year. Using parentheses when entering the formula into a calculator is important because the formula needs to be evaluated in a specific order.
Instructions
1. Enter the principal amount into the graphing calculator. For example, if $1,000 was initially deposited, enter “1000.”
2. Enter (1 + (r/n)) into the graphing calculator. For example, if the annual interest rate is 2 percent and interest is compounded quarterly, enter (1 + (0.02/4)). 2 percent is the same as 0.02 and interest that is compounded quarterly means that is is compounded four times per year.
3. Press the “^” key for exponentiation.
4. Enter “(n*t)” into the graphing calculator. For example, if interest is compounded quarterly and the money will be in the account for five years, enter “(4*5).”
5. Press the “Enter” or “=” key on the graphing calculator. In the example, the balance of the account would be approximately $1,104.90 after five years.
Instructions
1. Enter the principal amount into the graphing calculator. For example, if $1,000 was initially deposited, enter “1000.”
2. Enter (1 + (r/n)) into the graphing calculator. For example, if the annual interest rate is 2 percent and interest is compounded quarterly, enter (1 + (0.02/4)). 2 percent is the same as 0.02 and interest that is compounded quarterly means that is is compounded four times per year.
3. Press the “^” key for exponentiation.
4. Enter “(n*t)” into the graphing calculator. For example, if interest is compounded quarterly and the money will be in the account for five years, enter “(4*5).”
5. Press the “Enter” or “=” key on the graphing calculator. In the example, the balance of the account would be approximately $1,104.90 after five years.
Graph on a TI84 Calculator
Math, statistics and calculus are all words that many students dread. However, math isn't so daunting if you understand how to use technology. Graphing calculators can perform a variety of functions, including the production of graphs. By learning how to use the functions of a graphing calculator, you are sure to simplify your math courses.
Instructions
1. Compile a list of data. Once you have the data, you are ready to proceed with the calculator. Data can come from experiments, an assignment or simply a textbook.
2. Enter your data into the lists by clicking the black button which says "Stat", select "1: Edit..."and then click "Enter". This will take you to your list section.
3. Enter data in L1 and L2. L1 will be your X-axis on the graph and L2 will be your Y-axis.
4. Click blue button that says "2nd", followed by smaller button above it, which says "Y=". You will find that above the "Y=", it reads "Stat plot".
5. Select Plot 1 and click "Enter". Turn the plot, or graph, on by highlighting "On".
6. Scroll down to "Type" to pick the specific type of graph you would like to use. The options are histogram, scatter-plot, line graph, bar graph, or box and whiskers.
7. Scroll down and verify that your X list is set to L1 and Y list is set to L2. This means that your X-axis will be the numbers you entered in L1 and your Y-axis will be the numbers you entered into L2.
8. Click the small gray button in the upper right corner that says "Graph". Your graph will appear.
Tips & Warnings
- For more advanced graphs, refer to your graphing calculator guide. According to Morton Bay College, check window values to ensure your graph will show up. Click "Window" and verify the X-min, X-max, Y-min and Y-max.
Instructions
1. Compile a list of data. Once you have the data, you are ready to proceed with the calculator. Data can come from experiments, an assignment or simply a textbook.
2. Enter your data into the lists by clicking the black button which says "Stat", select "1: Edit..."and then click "Enter". This will take you to your list section.
3. Enter data in L1 and L2. L1 will be your X-axis on the graph and L2 will be your Y-axis.
4. Click blue button that says "2nd", followed by smaller button above it, which says "Y=". You will find that above the "Y=", it reads "Stat plot".
5. Select Plot 1 and click "Enter". Turn the plot, or graph, on by highlighting "On".
6. Scroll down to "Type" to pick the specific type of graph you would like to use. The options are histogram, scatter-plot, line graph, bar graph, or box and whiskers.
7. Scroll down and verify that your X list is set to L1 and Y list is set to L2. This means that your X-axis will be the numbers you entered in L1 and your Y-axis will be the numbers you entered into L2.
8. Click the small gray button in the upper right corner that says "Graph". Your graph will appear.
Tips & Warnings
- For more advanced graphs, refer to your graphing calculator guide. According to Morton Bay College, check window values to ensure your graph will show up. Click "Window" and verify the X-min, X-max, Y-min and Y-max.
Shade on a Graphing Calculator Using the Shade Command
Shading on a graphing calculator is a great way to visually indicate overlap, whether between two inequalities or two lines. For instance, if you want to shade the space below one equation and above another, you can use your graphing calculator to indicate where these points are located. You may have to do such work in advanced math or science courses, and shading on your calculator makes it possible to check your work.
Instructions
1. Access the y=? portion of your calculator, and enter the functions of interest. Let's say, for our purposes, that you want to shade the area above y=x^2 and below y=x. Enter x^2 into the Y1= prompt, and enter x into the Y2= prompt.
2. Access the "draw" menu, and from the menu, select the "Shade" command. Your calculator will display the Shade function along with open brackets.
3. Enter the function, first, that you would like to shade above, then enter the function that you would like to shade below. In this example, the prompt would look like Shade(Y1, Y2).
4. Hit the "Enter" button. The calculator will shade as you requested.
Instructions
1. Access the y=? portion of your calculator, and enter the functions of interest. Let's say, for our purposes, that you want to shade the area above y=x^2 and below y=x. Enter x^2 into the Y1= prompt, and enter x into the Y2= prompt.
2. Access the "draw" menu, and from the menu, select the "Shade" command. Your calculator will display the Shade function along with open brackets.
3. Enter the function, first, that you would like to shade above, then enter the function that you would like to shade below. In this example, the prompt would look like Shade(Y1, Y2).
4. Hit the "Enter" button. The calculator will shade as you requested.
Do Fractions on the TI-84 Plus Graphing Calculator
Fractions are a basic function of mathematics. A fraction compares the relationship between parts and whole. The fraction one-fourth denotes that one part out of four is present. Inputting fractions into a TI-84 Plus graphing calculator requires extra attention due to the order of operations. However, once you get the hang of it, doing fractions on the TI-84 Plus is quite simple.
Instructions
1. Consider the mathematical function of the fraction. You must understand the nature of the math problem to input it into the calculator.
2. Turn on your TI-84. Your calculator should open with a blank screen. If not, hit the "Clear" button until your calculator shows a blank screen.
3. Enter the math problem in the calculator exactly as it is given to you. When you get to a fraction, place an open parenthesis before the first number in the fraction. Continue to enter the remainder of the fraction value and then place a closed parenthesis after the last number in the fraction. For example, "2 + 3/4" should be entered as "2+(3/4)."
4. Solve the problem by pressing the "Enter" key on the lower right-side of the keyboard.
5. Convert your solution back into a fraction by pressing the "Math" key and then selecting "1".
Instructions
1. Consider the mathematical function of the fraction. You must understand the nature of the math problem to input it into the calculator.
2. Turn on your TI-84. Your calculator should open with a blank screen. If not, hit the "Clear" button until your calculator shows a blank screen.
3. Enter the math problem in the calculator exactly as it is given to you. When you get to a fraction, place an open parenthesis before the first number in the fraction. Continue to enter the remainder of the fraction value and then place a closed parenthesis after the last number in the fraction. For example, "2 + 3/4" should be entered as "2+(3/4)."
4. Solve the problem by pressing the "Enter" key on the lower right-side of the keyboard.
5. Convert your solution back into a fraction by pressing the "Math" key and then selecting "1".
Put Base Log on Graphing Calculator
A base log is a log where the subscript small number next to the log is present. If it is not present, then it is a base 10 log. Use your graphing calculator to figure out what the base log equals. In order to understand how to enter the information, label the base and the number next to it. Call the base "b" and the number next to the base "x."
Instructions
1. Press the log button.
2. Enter the number next to the base, x.
3. Press ")."
4. Press the division sign.
5. Enter the base, b.
6. Press ")." Your calculator should read: "Log(x)/(Log(b)."
7. Press "=."
Instructions
1. Press the log button.
2. Enter the number next to the base, x.
3. Press ")."
4. Press the division sign.
5. Enter the base, b.
6. Press ")." Your calculator should read: "Log(x)/(Log(b)."
7. Press "=."
Using Tan on the Graphing Calculator
Decades ago, students needed to painstakingly use a slide rule to find the answer to a trigonometric problem involving tangents. Now, a graphing calculator makes the process quick and easy.
Finding an Unknown Side
As a trigonometric function, tangent (Tan) represents the ratio between the side opposite an angle in a right triangle and the side next to the angle. Therefore, if you need to find the length of a side in a triangle, you would press the "Tan" button on the calculator, enter the angle measure, close the parentheses, and hit "Enter."
Finding an Unknown Angle
The reverse process is used to find an unknown angle. Divide the side opposite the angle by the adjacent side. Then use the second function of the tangent button (called the arctan or inverse tan) by pressing "2nd" and then "Tan." Enter the number that you got by dividing the sides, close the parentheses, and press "Enter."
Tangent Graph
The "Tan" button on the graphing calculator can also be used to graph a tangent function. For example, to graph 2tan(x) -3, you would press "y=" and then enter the function using the "Tan" button to represent the tangent in the equation. Pressing "Graph" will then display the function visually on the coordinate plane.
Finding an Unknown Side
As a trigonometric function, tangent (Tan) represents the ratio between the side opposite an angle in a right triangle and the side next to the angle. Therefore, if you need to find the length of a side in a triangle, you would press the "Tan" button on the calculator, enter the angle measure, close the parentheses, and hit "Enter."
Finding an Unknown Angle
The reverse process is used to find an unknown angle. Divide the side opposite the angle by the adjacent side. Then use the second function of the tangent button (called the arctan or inverse tan) by pressing "2nd" and then "Tan." Enter the number that you got by dividing the sides, close the parentheses, and press "Enter."
Tangent Graph
The "Tan" button on the graphing calculator can also be used to graph a tangent function. For example, to graph 2tan(x) -3, you would press "y=" and then enter the function using the "Tan" button to represent the tangent in the equation. Pressing "Graph" will then display the function visually on the coordinate plane.
Solve Inequalities With Graphing Calculators
Solving an inequality is similar to solving a mathematical equation. The difference is that an inequality uses a greater than or less than sign instead of an equals sign. These equations yield a range of answers instead of a single value. When you have a system of two inequalities, a graphing calculator can help you find the answers by graphing the two inequalities on the same graph.
Instructions:
Texas Instruments TI-83 or TI-84
1. Press the "On" button to turn on the calculator.
2. Push the "Y=" button.
3. Enter the first inequality into "Y1=." Navigate to the symbol in front of "Y1."
4. Press "Enter" to adjust the shading of the equation. For an inequality with a "greater than" sign, such as "y > x - 3," press "Enter" twice. For an inequality with a "less than" sign, such as "y < x + 4," press "Enter" three times.
5. Press the down arrow button to navigate to "Y2." Repeat steps 3 and 4 for "Y2=" using a second inequality.
6. Press "Graph." The overlapping shaded area is the answer.
Hewlett-Packard HP-39g or HP-40g
1. Press the "On" button.
2. Press the "Aplet" button. Navigate to the "Dual Inequalities" aplet.
3. Press "Start." A note will appear on the screen. Hit the "Enter" button.
4. Enter the first inequality into "F1(X)=." Press "Enter" and type the second inequality into "F2(X)=."
5. Press the "Views" button. Select the types of inequalities from the list.
6. Press "OK." The double-shaded area is the answer.
Casio FX-9860G or FX-9860GII
1. Press the "AC" button to turn on the calculator.
2. Navigate to the "Graph" icon on the screen. Press the "Exe" button.
3. Press "F6" to navigate to the next screen. Select the "F" button that coincides with the inequality sign of the first inequality. Enter the first inequality and press the "Exe" button.
4. Repeat Step 3 for each additional inequality.
5. Press the "Shift" button. Then press the "Menu" button. Select "F1" to turn on inequality shading.
6. Press the "Exe" button, followed by the "F6" button. The shaded area is the answer.
Instructions:
Texas Instruments TI-83 or TI-84
1. Press the "On" button to turn on the calculator.
2. Push the "Y=" button.
3. Enter the first inequality into "Y1=." Navigate to the symbol in front of "Y1."
4. Press "Enter" to adjust the shading of the equation. For an inequality with a "greater than" sign, such as "y > x - 3," press "Enter" twice. For an inequality with a "less than" sign, such as "y < x + 4," press "Enter" three times.
5. Press the down arrow button to navigate to "Y2." Repeat steps 3 and 4 for "Y2=" using a second inequality.
6. Press "Graph." The overlapping shaded area is the answer.
Hewlett-Packard HP-39g or HP-40g
1. Press the "On" button.
2. Press the "Aplet" button. Navigate to the "Dual Inequalities" aplet.
3. Press "Start." A note will appear on the screen. Hit the "Enter" button.
4. Enter the first inequality into "F1(X)=." Press "Enter" and type the second inequality into "F2(X)=."
5. Press the "Views" button. Select the types of inequalities from the list.
6. Press "OK." The double-shaded area is the answer.
Casio FX-9860G or FX-9860GII
1. Press the "AC" button to turn on the calculator.
2. Navigate to the "Graph" icon on the screen. Press the "Exe" button.
3. Press "F6" to navigate to the next screen. Select the "F" button that coincides with the inequality sign of the first inequality. Enter the first inequality and press the "Exe" button.
4. Repeat Step 3 for each additional inequality.
5. Press the "Shift" button. Then press the "Menu" button. Select "F1" to turn on inequality shading.
6. Press the "Exe" button, followed by the "F6" button. The shaded area is the answer.
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