 Hey everyone, welcome back to Tutor Terrific. In this video, I'm going to do a calculator tutorial and that calculator is the Texas Instruments TI-84 Plus, the original version which ran on AAA batteries. The basic design for the interface of this calculator is equation operating system and so you're going to work with expressions, you're going to plug those expressions in and then you're going to press enter to evaluate them. Now that contrasts with the algebraic operating system which you do one algebraic operation at a time and then see how the result is affected by that operation. Sometimes it feels like you're doing certain things in reverse. For example, plugging in the input to a trig function like sine and then pressing sine to evaluate it. The sine of that input, there's other things with squaring numbers and such where it feels the same way and algebraic systems but the equation operating system is good for more advanced calculations where you want to see the whole thing before you evaluate it so you can check it for errors and then go over editing and inserting things in a little later. So turning the calculator on, of course the on button in the bottom corner like all Texas Instruments systems and that cursor shows up. If you want to turn the calculator off you can simply just leave it idle and after a few minutes it will automatically shut off or you can press the second button. You know the second button is pressed when that arrow is in the cursor and if you press the second button what you'll activate is the action of any of the blue text above each button. So if I press the on button right now it will activate the off and it will turn the calculator off. So that's your basic on and off. Let's go over some basic operations. Make sure that our order of operations is working correctly. For example, simple algebraic operations input. Here they are over here. Divide, multiply, minus plus. Let's do 7 times 5 minus 3. So if it does this in the correct order by multiplying before subtracting you should get 32 and if it does it in the wrong order or it does the subtraction first you would expect to get 14. So let's press enter like this and we get 32 like we expect. Now if you'd like you can do more calculations on this same window since it's so large without having to erase anything. So let's try another one. 9 plus 5 divided by 6. Press enter and you can see that calculation on the same screen. Now if you want to get rid of all these operations you can of course press clear and all of that goes away in the windows blank again. If you'd like to recall for example an old entry you can do that as well by first pressing the second button and then pressing entry. It'll retrieve your last entry you had and you can evaluate it again but you can go back farther into the memory recesses of this calculator by pressing second entry a second time you'll go back to the previous calculation before that and before that and before that and you can do that as much as you'd like until you get to the beginning of the calculator's memory. Now you can of course clear your memory but I'm not going to get into that in this video. So that's your basic operations but there's many more we can do that are basic like squaring something for example six squared that's a very popular one so it's up here in the front and we can of course evaluate that the same way by pressing enter we can do a square root as well we would press the square root button first and then let's do 64 for example you can leave the parentheses open but it's good practice to close it in case you have more complicated calculations and there you go you can press that and you get eight so there's some basic operations for you now I've shown you the second button but I also want to show you the alpha button the alpha button is very useful as you can see this will activate all of the green text now most of these are just letters of the alphabet now how this is actually useful is for storing values maybe this could come in handy later on for you let's just say 44.8 is the number you need well you can actually store that as a letter so you don't have to type those four buttons you just press a particular letter the store a value you press the store button down here okay which gives you that arrow then you need to click the letter you want to store it as and so you would press alpha you can see when alpha is pressed you have an A in the middle of the cursor that lets you know you're an alpha let's say I want to store that as a letter A okay so I click that now you see after you do alpha one time or the second button one time it will revert back to normal button pressing and you don't see any of those special symbols anymore in the cursor so if I press enter now it just gives me back the number but it is stored as A as well so if I call A in an expression it will be equal to 44.8 so check this out let's say I just wanted to type the letter A and then press enter it gives me its value 44.8 let's say I wanted to use A in an expression 1 plus alpha A minus 6 okay you should expect to get 39.8 if you do this boom right there so it's using A as 44.8 and that is perfectly fine now A will be stored as 44.8 until you reset it to be something else so just keep that in mind and you have many many letters 26 of them to pick from to store lots of different things so just understand that and it's really nice okay so those are some basic features now what if you have a really complicated calculation and you made a mistake you're like oh no I don't want to type the whole thing again some people just press clear and just clear the whole thing out and start over you do not have to do that so let's say I'm like doing some really complicated thing with finances and I've got lots of things I'm adding together multiple products for example like this okay and I make a mistake oh darn it I wanted to put 0.9 versus 0.8 because it's going to calculate it wrong well don't just press clear hold on let me show you and go backwards with these with the pad buttons you can go up down left or right you can go to your mistake let's say you wanted that to be 0.9 instead of 0.8 you put the cursor right on that 8 and press 9 and now it's at 9 so you didn't have to redo the whole thing you didn't have to retype it in you could just go there and press 0.9 what if it wasn't 0.9 but it was 0.95 oh no what do you do well there's something you can do and that's the insert button above the delete button which will go over in a second you can see INS if I press second delete now you see the cursor is not a bit black box but a little line so what that's going to do in a little underscore actually that's going to do is put something in front of what's blinking so if I type 5 it inserts that character in its place allowing you to evaluate it now and you can do that insert as many times as you want so I press second delete and I type a bunch of numbers you see it's putting all of those numbers in after the first one now let's say oh shoot I have something I don't want I need to get rid of it before I calculate it let's say you want a 0.2 instead of 0.25 well you can just press DEL and it will delete that character one of the basic operation I'd like to show you guys is how you can use your previous answer it's really really helpful so let's calculation again 7 times 5 minus 3 equals 32 I can use that previous answer of 32 in multiple different ways if I just press an operation so just divide what's going to do is it's going to load my previous answer and say what would you like to divide it by so that previous answer is always stored as A and S well divided by 4 and I should get 8 which I do but there's more to it than that I can plug a previous answer in anywhere in another expression so for example 7 times 5 minus now let's say I want to take that answer I know it's easy to type an 8 but just for the sake of the exercise let's get the previous answer loaded now what I do is I press second and down here by the way there's two minus signs here this is the minus and this is the negative button down here in parentheses you can see A and S is above that so if I press second minus sign now I've loaded my previous answer to my last calculation and by the way this is only the very last calculation you've done so now it's 27 7 times 5 minus 8 is 27 so that's a useful tool for doing complicated calculations you want to do parts at a time you can load the previous answer into your next expression ok now what I want to show you guys it's really important it's called the mode window that's kind of your settings window for your calculator there's a couple that are really important for example look out everything is notated in sort of row format so each setting is row of this mode window normal scientific and engineering is the type of calculations you're doing and how they're viewed the next one down is kind of important it's the number of decimal places that are going to default on the calculator or numbers that might have an infinite repeating decimal or non-repeating irrational decimal you can decide how many decimal places after the decimal you would want to default to you can go up to 9 to the floating point which will just truncate it where it needs to be if it's a finite decimal or not so that's one important setting another really really important setting is the third one down radian versus degree now these are two different units for angles and if you want to be in radian mode all the angles you plug into any of the trig functions sine, cosine, tangent, etc will be treated as in radians versus if you clicked over here you press the right arrow to highlight degree and press enter now it switches the setting to degree mode so now the angles you plug in will be treated as in degrees there's no symbol written you just have to know what mode you're in so by the way I didn't state this but everything that is selected right now as the setting is highlighted in black so if I move off the degree you can see that the degree is now selected versus radian mode if I press enter again on radian it will switch back to that to get out of the mode sorry, mode window and then it will teach you a new button called quit if you press second mode it will quit whatever you're doing and take you back to that main page now since we're talking about trig functions let's do a few of those to make sure you understand where they are in the calculator and how to get them remember right now we're in radian mode and this will give me an opportunity to show you where pi is as we know pre-calendar algebra 2, the unit circle fractions of pi over useful angles in radians so all the trig functions that you can see right here are a sine, cosine, and tangent they have their own buttons so let's just type one in, we're going to type the trig function first unlike algebraic operating systems calculators and then we're going to plug in let's say pi over 2 well where's pi? pi is above the carrot button which I'll get into a little later you can see it there in blue right above it next to the H so I need to press second carrot and then I have my pi and then I can type divided by 2 to get the over 2 and we should get 1 for this if we're in radian mode correct now let's say I was accidentally in degree mode when I did that so I'll switch over to degree mode quit to get out of that window and I will recall the previous entry now I'm in degree mode I get a very different answer and this is an infinite decimal going as far as possible because I'm in floating point mode and notice that I'm looking at pi over 2 degrees 1.57 degrees that's what the sign of that is so you've got to make sure you're in the correct mode now if I did the sign of 90 which is equal to pi over 2 radians it's reading it in degrees so I should get 1 so that's what I'd expect so things are the same for cosine and tangent now how do you get the reciprocal trig functions secant, cosecant and cotangent well there's no special button for them so what you have to do in this calculator is literally press well you have one or two ways to do it I'm going to do it the fraction way cosecant will be the reciprocal of sine or in other words 1 over sine so if I plug in 90 because I'm in degree mode this will be the cosecant of 90 which is equal to 1 over sine of 90 which would also be 1 same is true for secant you would do 1 over cosine and cotangent you would compute 1 over tangent so there's another way to do it though if you prefer exponents and that would be to use the negative 1 power so if I wanted the cosecant of 90 I could do the following I could write sine of 90 inside a set of parentheses and then I could do this which may be good for you the negative 1 button so this is like the negative 1 power which would be cosecant of 90 so you could do it that way as well but you'll notice and I might have already noticed that above the sine cosine and tangent there are sine negative 1 cosine negative 1 and tangent negative 1 buttons those are not reciprocal trig functions guys those are the inverse trig functions so we're in degree mode we would expect the inverse sine of 1 90 degrees so I'm going to press second sine and I'm going to plug in 1 because that's my value at 90 degrees and I should get 90 out perfect so now you know that those second buttons are for the reciprocal trig functions now if you wanted to do an inverse cosecant you would have to do 1 over inverse sine but those don't come out much so I don't anticipate you needing those so just so you know those are the trig and inverse trig functions and how they are used let's go over now some other types of functions power functions or log functions so to get any power note that there's a special shortcut not only for the squared and the negative 1 powers but also for the third power it's commonly used so let's say I wanted to find 9 to the third power well there's a special tool for that you go to that math menu and as you can see in this first one we have the third choice as 3 that's the cubic power and so we get 729 for that notice also right underneath that in the math window there is a special button for the cube root and for the xth root the cube root of course we know what that does if I press 4 right now and then type in 27 I would expect to get 3 when I plug that in perfect well if you wanted a higher order root well you would click math and then you click the 5 but before you click the 5 and you go to this menu you need to click what power you type in what power you want to use what degree of your root rather so let's say I wanted to find the 5th root of 32 so I type 5 and then you go back to the math menu click number 5 now what it's going to do is it's going to see that as the 5th root it's taking that 5 to be the value of x notice that there's no parenthesis here I've never understood that but it's not like one's really needed but I always do it just to be extra safe you get a 2 for that what if you wanted a higher power not a higher fractional power a radical but a higher power well I've shown you this before but it's the care button so what I do let's say I wanted 5 to the 5th power I would press 5 and then I would press the care button and then I would press 5 again so this will evaluate 5 to the 5th power 3125 so you can get any power that way now what about log functions there's a couple log logarithm function buttons here on the side and I want you to know that this calculator cannot find the log to any base it defaults to log base 10 that's the LOG button and log base E which is the of course natural log button so if I type log I type in 100 it's going to evaluate the power that you need to raise 10 to to turn it into 100 which would of course be 2 so this is log base 10 the common log of course we could do a natural log as well and just so you know there is a button for E and that button is second divide you see that E up there press second and then the division button and if I evaluate the ln of E I should get a 1 perfect so what if you did need to find the log of a different base than 10 or E well you can do it using this work around formula called the change of base formula so let's say you want to calculate log base 3 of 27 which we know is 3 so you can't use base 3 so you'll have to change it to base 10 what you do is you will click or you can change it to the base ln but we'll do base 10 just for simplicity you would type the log of the argument you're trying to find which is 27 and you'll divide that by the log base 10 of the old base this will evaluate the log base 3 of 27 so that's the work around and it also works for ln this is the exact same way you can use the change of base formula for the log of a certain base to any log of any other base ln of 3 and you would get 3 as well so that's the work around for finding the log of a different base on this calculator now I want to move on to the last topic of this video which will be graphing features so this is a graphing calculator you want to know that it can graph well that's totally true and that's why it has a mostly square screen to plug in a formula you want to graph if you're going to click this y equals button here that gives you all these different options for graphing you can graph up to many many many graphs at the same time if you scroll down it keeps going all the way to 10 you can have 10 different graphs at one time and 3 different plots which we'll get into in another video with statistics so let's say you wanted to graph a nice curve let's do x cubed minus 4x how do you get that x that's a variable it's this button here now I've shown you where the cube is math 3 I like it because it's nice and simple don't have to use a carrot for the cube button minus 4x squared so minus 4x again squared plus 1 ok so it's there I see it on a graph a Cartesian coordinate plane I click this graph button on the opposite side of the calculator now what this shows me is a 10 by 10 well really 20 by 20 grid 10 tick marks on each side of the origin of the x-axis same on the y-axis however you can see that they're not evenly spaced the y-axis is a little bit squished to get the same number of tick marks so they're not evenly spaced in both axes they're not on the same scale but it's close enough and you can see the tick marks as the dots let's say you wanted to zoom in or change the window I'm going to show you to change the window first so you can see maybe a different set of tick marks so right now what this window shows is that the minimum x tick mark the leftmost tick mark is negative 10 the rightmost tick mark x-axis is positive 10 and the change in tick mark is 1 I can change all of that let's say I wanted to just go from negative 5 to 5 I would have to delete the 0 by the way and on the y-axis I want to go from negative 7 to 7 now I know this will be even farther out of scale but just to give you an idea you will click graph so you can see now that it's only going from negative 5 to 5 on the x-axis and negative 7 to positive 7 on the y-axis let's say you wanted to undo those changes quickly well here's what you could do the zoom button allows you to zoom in and out or zoom to any particular setting default and that would be for us to get back to where things were zoom 6 as soon as you click that it will graph it at that new zoom if you click on window you'll see that it has reset my window let's say I wanted to change how the x-tip mark increments not by 1's but by 2's so I shouldn't see half as many tick marks and that's exactly what I do each tick mark represents 2 units on the x-axis instead of 1 I can also do that on the y similarly by changing y-sc let's change it to 4 so we should see very few tick marks on the y-axis so each tick mark is now 4 apart from any other one around it and again pressing zoom 6 reset all of those settings back to the original now I can analyze my graphs many ways with the calculate feature which is second trace but I also want to show you trace real quick if you click trace you can follow along on your curve and look at the x and y value at very particular spots now it's very pixelated so most of these spots have no meaning maybe you can get a general idea but the value is changing as you go from left to right but let's say you want to calculate particular spots particular locations such as calculating the minimums and maximums of the graph well this time you'll click second trace and you get this window of things you can calculate number one thing I want to show you is how to calculate a minimum and a maximum so you go down to 3 you click 3 and now you're looking at your graph and it's asking you left bound or right bound so what that means is since we're calculating a minimum right now go back just to double check it's a minimum we're calculating we want to get on the left side of that visually understood minimum which is right here anywhere on the left of it press enter and then it says right bound so you want to move your cursor so that you're on the right side of that minimum you can see these two arrows it's going to calculate the minimum value between those two spots and it says guess that's not really a guess it's actually calculating it press enter again and then the minimum y value is there and where it occurs is the x value the same can be done for a maximum if you press second trace and then you click 4 now we're looking for a maximum we know where it is it's right there on the y axis so we want to get on the left side of it then right bound, get to the right side of it press enter and then press enter again and it finds that particular maximum y value of 1 and then where it occurs now this particular let me show you 1.4 it looks like it's right at 0 1.45 is negative 6 that's exponent meaning scientific notations specifically negative 6 so this is basically 0 it should be exactly 0 but the way the algorithm is generally calculated you can get that a little off that's just a small error so another important thing if you press clear this will all go away all this analysis would be good to calculate maybe your x intercepts those would be important so you press second calculate 2 we'll give you the option to calculate the zeros again you want to get on the left side over here move your cursor so that you're next to it not beyond any other 0 to the left press enter and you want to move to the right side of that 0 just right of it press enter again and then press enter a third time and it calculates the very spot where that 0 occurs so this 0 would be 3.9 3.5 etc so those are two important things you can analyze there are many more but we'll get into that detail in another video you can also check my TI83 plus graphing features video which goes over all of this on that calculator basically the same configuration now let's say you wanted to graph a trig function like side of x for example and I will increase the amplitude so it shows up better on the normal window 3 sin of x now by the way graphing trig functions it's better to be in radian mode so you can go to that mode window anytime and make sure radian is selected it wasn't due to my other video parts so we need to select that then we'll go back to y equals so I'm going to graph 3 sin x now when you graph this in the normal window with the graph button hopefully you can tell but the tick marks on the x axis aren't really lining up very well or the y axis for that matter with the function itself y axis you can tell that it goes all the way up to 3 and down to negative 3 that's the amplitude of the function but the tick marks on the x axis really don't line up at all because they're just whole numbers if you know and if you've worked with a sine graph or any of the trig function graphs what you need to pay attention to are multiples of half of pi and those aren't showing up here really well but there's a special zoom feature for that and it's called zoom trig it's the 7th option if you click 7 look at the tick marks on the x axis and the y axis much different they're much more spread out and on the x axis every tick mark is pi over 2 separated from every other tick mark 0 in the middle, pi over 2, pi 3 pi over 2 and 2 pi so you see a whole period on each side of the y axis for the sine graph in addition the y axis tick marks go from negative 4 to 4 so it's more useful for spreading out the trig function so it sort of fills the frame as we say and that's just a special feature of these calculators that let you graph trig functions much more easily alright guys, that's all I wanted to show you to give you sort of a quick introduction over view to this calculator it's a fantastic calculator, again to turn it off you press second and then on so I hope you enjoyed this video guys give it a thumbs up, give it a comment let me know what else you want to see on this calculator in the next tutorial video thank you guys so much for watching this video this is Falconator, signing out