Why do I need to log in?
A. SET UP
B. General Information
C. Complex Numbers
D. Solve Systems of Equations
E. Solve a Quadratic or Cubic Equation
F. One and Two Variable Statistics
G. Regression
H. Calculate a Derivative
I. Solve a System of Four Equations
J. Calculate an Integral
SET UP on the Sharp EL 546WB Calculator
This button allows you to change degrees to radians to grad mode. You do not need to use this route, though. A shortcut is accessible by pressing 2ndF and then the decimal point. That accesses DRG►.
To use the SET UP route, press the SET UP button.
Press the = button while the 0 under DRG is flashing. Now use the left or right arrow keys to select the
mode you want.
The SET UP button allows you to change your calculator to fixed, scientific, exponential mode.
Use the right arrow button to move to FSE.
Press the = button while the 1 under FSE is flashing. Now use the left or right arrow keys to select the mode you want.
The fix choice fills the screen with decimal places. Now you can go back into SET UP and choose TAB which will allow you to choose how many decimal places you want the calculator to use for all numbers.
The SCI choice changes your calculator into Scientific Notation mode.
The ENG choice changes your calculator into Engineering mode.
The NORM1 and NORM2 choices get your calculator out of any of these modes back to looking a “normal calculator” look. NORM1 should be your choice.
The Sharp EL 546 WB Calculator in general
DON’T THROW THOSE INSTRUCTIONS AWAY!!
In general, to make a choice press the = button. To see more choices, use the left and right arrow keys.
The calculator has six different modes: NORMAL, STAT (statistics), EQN (equation), CPLX (complex), MAT (matrices), and LIST. Each has its own purpose and will be used at different points in your course. Switch modes by hitting the MODE button and then using the up/down/left/right arrows along with the = button or by pressing the number of the corresponding mode (e.g. 3 for EQN). In general, use NORMAL mode (MODE 0).
The 2ndF button allows access to secondary functions (written in orange above the buttons). For example, to find the square root of 5 hit the 2ndF button then the x ^{2} button. A root sign will appear in the display. Hit 5 and then = to calculate the square root of 5 (2.236...). To turn off the calculator hit 2ndF then ON/C.
Uing brackets can make calculations easier to perform. Sometimes they are necessary to get the correct value. This is because the calculator follows the BEDMAS order of operations. An example of this would be dividing 1 by 2+3. The correct answer is 0.2. If you type this in as 1÷2+3 the answer will be 3.5 which is incorrect. The calculator divided 1 by 2 and then added 3 to the result. We want 1 divided by 2+3 so we enclose the 2+3 in brackets. Typing it in as 1÷(2+3) we get 0.2, the correct answer. This is a simple example of how brackets can be used in complicated calculations.
The MODE button allows you to enter and calculate with complex numbers in polar or rectangular form. Choose MODE and then the "3" CPLX option.
Once you do that, you may choose polar or rectangular formats. To choose polar format, press 2ndF and the 8 key to access →rθ. You will see an “rθ” appear in the upper left corner of the screen. To choose rectangular format, press 2ndF and the 9 key to access →xy. You will see an “xy” appear in the upper left corner of the screen.
That means the “xy” is in the upper left corner of the screen. This does not affect the normal arithmetic calculations you need to do. But it also activates the complex number buttons on the calculator. One of those is the “i” key which is available in regular computation as the fraction key.
Let’s say you want to enter 2 + 8i. You would type in 2 + 8, and then press the a b/c key for i. Press the = key. The calculator tells you “2” which is the real number part of this complex number. Now press the 2ndF and then the Exp key. This gets at the ←,→ choice. This tells you the second part of the answer, which is “8i”.
To multiply (4 + 6i)(6 – 5i), enter the numbers. Make sure you use brackets as shown! Press the = key. You get 54. Then press 2ndF and Exp for the ←, → choice. You get +16i. So the answer is 54 + 16i.
For any entry of complex numbers in rectangular form, use brackets around each complex number, as in (4 – 2i).
That means the “rθ” is in the upper left corner of the screen. Again, this does not affect the normal arithmetic calculations you need to do. But it also activates the complex number buttons on the calculator. One of those is the angle key which is the D^{o}M’S key in usual computation.
Let’s say you want to enter 2 angle 30^{o}. First make sure you are in degree mode. Then type in 2, press the angle key, and then 30. Press the = key. The calculator tells you “2” which is the real number part of this complex number. Now press the 2ndF and then the Exp key. This gets at the ←, → choice. This gets at the second part of the answer, and which is “angle 30”.
To multiply (5 angle 30^{o})(6 angle 120^{o}), enter the numbers. Press the = key. You get 30. Then press 2ndF and Exp for the ←, → choice. You get angle 150. So the answer is 30 angle 150^{o}.
Say you want to change 30 angle 150^{o} to rectangular format. Make sure you have entered that complex number. Then choose →xy. The calculator tells you -25.98 (rounding to two decimal places). Then access the complex part using ←, →. That gives you 15i. So 30 angle 150^{o} = -25.98 + 15i.
Say you want to change 4 – 7i into polar format. Enter the complex number. Choose →rθ. Press the = key. You get 8.06 angle -60.26^{o}.
Solve a System of Two or Three Equations with the Sharp EL 546WB Calculator
The MODE button allows you to solve a system of linear equations. Choose MODE and then EQN.
Let’s say that you are working with two linear equations. They must be in this format:4x + 5y = 352x – 6y = 23Go into MODE and EQN and choose 2-VLE. (That’s for 2 equations. You would choose 3-VLE for solving a system of 3 linear equations.)The calculator will lead you through the solution by asking for the numbers. Enter the 4, 5, 35, 2, -6, and 23 in that order. Press the = button to move from one choice to the next. The calculator gives you the answers x = 9.6, y = -0.6 (these are rounded to one decimal place). Press the = button to move from the x to the y values. The det (determinant value) comes up next. Then it cycles through again. The calculator stays in this mode until you go back to MODE and choose NORMAL.
Solve a Quadratic or Cubic Equation with the Sharp EL 546WB Calculator
Let's say you want to solve a quadratic equation. It must be written in descending order, like 5x^{2} - 8x - 1 = 0. Go into MODE. Use the right arrow key to scroll to choice 3, EQN. Press the = key to choose that mode. That leads to more choices, and we want choice 2 QUAD. Enter the numbers 5, -8, and -1 in that order. Notice that those are the numbers used in the quadratic equation.
So for a?, type in 5 and press the = key.
For b?, type in -8 and press the = key.
For c?, type in -1 and press the = key.
The calculator states the answers:
X1 = 1.716515139 (Now press the = key to get the next answer) X2 = -0.116515139
Let’s say you want to solve a cubic equation. It must be written in descending order, like 4x^{3} + 3x^{2} – 4x – 1 = 0. Go into MODE. Then use the right arrow key to scroll to 3, EQN. Press the = key. That leads to more choices, and we need to choose 3, CUBIC (again, use the right arrow key to scroll to that choice).
The calculator will lead you through the solution by asking for the numbers. Enter the equation numbers 4, 3, -4, and -1 in that order. Press the = button to move from one choice to the next.
The calculator gives you the answers:
X1 = -1.3526517 X2 = 0.826320536 X3 = -0.223668836
CAUTION
Say the equation was 4x^{3} + 3x^{2} – 4x + 1 = 0.
X1 = -1.517526486 X2 = 0.383763242 X3 = 0.383763242
EXAMINE THE SCREEN CAREFULLY ON THESE ANSWERS!!!
The answers for X2 and X3 look like they are exactly the same.
BUT......... For X2, an xy appears in the upper left corner. That is a clue that this is a complex number. To find the rest of the complex number, press 2ndF and then Exp. You should get + 0.132164836i.
So really X2 = 0.383763242 + 0.132164836i.
For X3, the same xy appears. Finding the rest of that number, you will get X3 = - 0.132164836i.
So really X3 =0.383763242 - 0.132164836i
One and Two Variable Statistics on the Sharp EL 546 WB Calculator
As before, go into MODE and choose STAT and SD. Clear the memory to enter this new data. You will be entering these pairs of numbers in an (x, y) format, and that would be the STO key which is now (x, y) in STAT mode.
Enter 90, then press (x, y), then enter 5, and then press DATA. Enter 80, then press (x, y), then enter 2, and then press DATA. Enter 70, then press (x, y), then enter 1, and then press DATA. Enter 60, then press (x, y), then enter 6, and then press DATA. Enter 50, then press (x, y), then enter 3, and then press DATA. Again, these are one variable statistics, so they will all be values related to x.
Press the RCL key and then the statistic you want as before. Editing the values is possible using the up and down arrow keys.
Regression on the Sharp EL 546W Calculator
Finding the equation of a line of best fit is done through the STAT menu.
Say you want the linear line of best fit through these points. (They compare time T in seconds with distance D in cm of an object rolling down an inclined plane.)
Time T 1 2 3 4 5
Distance D 6 23 55 98 148
Choose MODE and STAT and LINE. Enter the data.
Type 1, then press (x, y), then type 6, then press DATA. Type 2, then press (x, y), then type 23, then press DATA. Type 3, then press (x, y), then type 55, then press DATA. Type 4, then press (x, y), then type 98, then press DATA. Type 5, then press (x, y), then type 148, then press DATA.
The equation of the straight line of best fit is y = a + bx. To find the value of a, press RCL and then a (which is the “(“ key in normal use). To find the value of b, press RCL and then b (which is the “)” key in normal use). To find the correlation value of r, press RCL and then r (which is the ÷ key in normal use).
a = -41.7 b = 35.9 r = 0.9837 (these numbers are all rounded). So the equation of the line of best fit is D = -41.7 + 35.9T.
The other lines of best fit work the same way.
For exponential regression, choose MODE, STAT, and then EXP. Enter the data as above. The equation of the line of best fit is y = a e^{bx}. [The e in this equation is the value 2.718....] Find the values of a, b, and r in the same way.
a = 3.84 b = 0.786 r = 0.9734 (these numbers are all rounded). So the equation of the line of best fit is D = 3.84e^{0.786}^{T}.
You would find the power line of regression in the same fashion. Choose MODE, STAT, and then PWR. Enter the data as above. The equation of the line of best fit is y = ax^{b}.
a = 5.93 b = 2.01 r = 0.9998 (these numbers are all rounded). So the equation of the line of best fit is D = 5.93T^{2.01}.
Calculate a Derivative with the Sharp EL 546W Calculator
Your Sharp EL 546W calculator can find the value of a first derivative for you. The calculator should be in NORMAL mode for this.
Say you wanted the value of the derivative of y = 4x^{2} + 8x – 3 at the point where x = 5.
To use this feature, first type in the equation. You would type into the calculator 4x^{2} + 8x – 3. To type the x in, use the green ALPHA button and then press the RCL button to access x. Type the entire equation in.
Then press the d/dx command. You will find this via the calculus key, the one above the log key. Press the 2nd F key and then this button to access the d/dx command.
The calculator will now ask some questions. The first “X = ?” is asking for the number value that you want. We want the value of the derivative at x = 5, so type in 5 and press the = key.
Then the calculator asks for the value of dx. The value of dx should be very small. You may type in a very small value or simply accept what the calculator offers. Press the = key.
The answer we get is 48.
The calculator is using an approximation formula to come up with this value. See the calculator instructions for the formula. The formula works well for smooth continuous functions.
Solve a System of Four Equations Using the Sharp EL-546W Calculator
The Sharp EL-546W calculator will solve a system of two or three linear equations using the 2-VLE and 3-VLE commands in MODE → EQN. But solving a system of four equations is not possible through this method.
This is where matrices come in. A matrix (plural: matrices) is an array of numbers. And you can set your calculator in matrix mode by choosing MODE and then choice 4 which is MAT, short for MATRIX. Press the = key to choose this mode. You will see the abbreviation MAT appear on the top right of the screen.
Let’s say we want to solve the system of equations 2p + q + 5r + s = 5 p + q – 3r – 4s = -1 3p + 6q – 2r + s = 8 2p + 2q + 2r – 3s = 2
The terms on the left side of the equal signs display an array of numbers. These numbers are the “coefficients” of the letter variables. These are highlighted in bold. 2p + 1q + 5r + 1s 1p + 1q – 3r – 4s 3p + 6q – 2r + 1s 2p + 2q + 2r – 3s
They will become this matrix on your calculator:
Enter these numbers, including negative signs into your calculator. To do that in MAT mode, start by pressing the down arrow on the top of the key pad. That starts the matrix entry, and the calculator begins by asking how many rows of numbers there are. Rows? We have 4. Press the DATA key (the M+ key, just above the right bracket button). The calculator then asks for Columns? We have 4. Press the DATA key again. Now to enter all these numbers. Press the DATA key after each number entry. 2 DATA 1 DATA 5 DATA 1 DATA These are the numbers from the first equation. Your calculator lets you know the location of these numbers. For the first 2, the calculator says “MAT 1,1 =”. This is Row 1, Column 1 in the matrix. For the 5, the calculator says “MAT 1,3 =”.
Continue entering the rest of the numbers, pressing the DATA key after each one. You are entering the numbers by rows. For the last number, the calculator said “MAT 4,4 =”, and you have entered -3. Press the DATA key, and you have finished entering the equation numbers in the matrix, so press the ON/C button. That exits you out of the number entry for the matrix. Press the MATH key and choose number 2 STO for store. This is to store the matrix numbers in the calculator’s memory. You have four choices. Let’s choose matA. Press the = key to make that choice.
If you think you made an entry error, you can always go back to survey your entries. Press the MATH key and then choice 0 for MAT. Choose matA and press the = key. Keep pressing the DATA key to scroll through all your entries. Correct any if necessary.
Now to enter the numbers that are on the right side of the equal sign in the equations. You will enter those in another matrix. This will be a matrix with 4 rows and 1 column.
So back to the main screen, press the down arrow at the top of the keypad, and enter Row = 4 and Column = 1, pressing the DATA key for each entry. 5 DATA -1 DATA 8 DATA 2 DATA This last entry will be “MAT 4,1 =”. Press the ON/C button to exit. We need to save this matrix as well. Choose MATH and STO (number 2). Let’s save this as matB.
We have now entered all the equation numbers in matrix form. Think of the 4 equations now in matrix form like this:
To solve for these 4 variables, we will need to move the large matrix on the left to the other side of the equation. In algebra, we would be moving it over by dividing since it is attached to the variables by multiplication. Dividing is the same as multiplying by its inverse (using the exponent of -1). This all looks like this:
In terms of the calculator, we need to multiply matA^{-1} times matB. Press the MATH key and then choose MAT. Press the = key to access choice 0 matA. Press 2ndF and then 2 to access the x^{-1}. Press the multiplication key. Press the MATH key and then choose MAT. Arrow to matB and press the = key to access choice 1 matB. Press the = key.
The calculator now provides the answers in matrix form. First it tells you that there are 4 rows. (Keep pressing the DATA key to scroll through the rest of the information). Then you find out there are 1 column. And the numbers are 2, 0.2, 0, and 0.8. In matrix form, this would look like this:
So you can see that p = 2, q = 0.2, r = 0, and s = 0.8.
SOME CAUTIONS: • Since there are 4 variables, there are 4 equations and each variable in each equation MUST have a number attached to it. If a variable is missing, assume the number is a zero. • Make sure you keep the letter variables in the same order in each equation. • In each equation, there must be the number by itself on the right side of the equal sign.
Calculate an Integral with the Sharp EL 546W Calculator
Your Sharp EL 546W calculator can find the value of a an integral for you. The calculator should be in NORMAL mode for this.
Say you wanted the value of the integral of y = 5x + 1 between x = 1 and x = 2.
To use this feature, first type in the equation. You would type into the calculator 5x + 1. To type the x in, use the green ALPHA button and then press the RCL button to access x. Type the entire equation in.
Then press the integral command ∫dx key. You will find this just above the log key.
The calculator will now ask some questions. The first “a = ?” is asking for the lower number value that you want to use. Type in 1 and press the = key. The calculator now shows "b = ?". That is asking for the upper number value. Type in 2 and press the = key.
Then the calculator asks for the value of n. This is like asking how many additions should be done between x = 1 and x = 2. We want a large number to make the answer accurate. The calculator by default shows 100 and that is adequate. Press the = key.
The answer we get is 8.5.