hello everyone and welcome to this lesson in this lesson we're going to talk about the syn graph now trigonometry is something new for grade 10 so i know it's a little bit weird these new syn cars and tan graphs but i'm going to do my best to familiarize you with it and to just show you that it's not that bad okay so a typical syn graph is going to look like this so we're going to draw a sin graph together so we need an x and a y axis first now on a normal graph we usually have x and a y axis and that's the same for the syn graph but on a normal graph your x values normally like 1 and 2 and 3 and your y values are like 1 and two on a sin cause and tan graph your x-axis is gonna be measured in degrees okay so you're gonna see things like 90 degrees 180 degrees 270 degrees 360. of course it could go backwards like minus 90 minus 180 minus 270 sorry that was a bit messy minus 360. your y-axis is going to usually go up in single numbers like 1 and 2 and -1 and -2 okay so we need to call on the calculator to help us work out where to put all the different dots so i'm going to get a calculator quickly now what i'm going to do is is i'm going to start off at 0 degrees okay so what i'm going to say is sin and then i'm going to put a 0 over there to say that it's the sin of 0 degrees so 0 degrees is where the x-axis and the y-axis meet and then i'm going to say equals and that's going to give me a value of 0. so what i'm going to do then is place a value at 0 and 0. so that's going to be over there then i'm going to go to the sin of 90 degrees okay so i'm going to say sin of 90 degrees and that's going to give me a value of 1. so when sin is 90 degrees then the y value is 1. now i'm going to go to 180 degrees next so if i say sin of 180 that gives me zero again okay so i can go put my little value over there and then i'm going to go to 270 degrees and 360. and if you put 270 degrees in the calculator you should get a y value of -1 over there and then if you put a x-value value of 360 then you're going to get a y value of zero so now we can connect that and so it will look something like that you just don't want to make it a straight line you don't want to do something like that you want to try make it as curvy as possible all right and then if we want to complete the left hand side then you would have to just type in the sin of minus 90. that would just give you a value of minus one sin of minus 180 is zero sin of minus 270 is one and then the sin of minus 360 is zero so it just con it just forms a continuous wave like that over there okay so notice how mine has a few untidy parts really doesn't matter guys that's not really what teachers are looking for you just want to make sure you can get it as neat as possible okay so that is a sun graph get very used to it the main things to realize is that a syn graph at 90 degrees it has a y value of one at 180 degrees it has a y value of zero at 270 degrees it has a y value of minus one and at 360 degrees it has a y value of zero now i could carry on with this graph i could have made this graph carry on and the syn graph will just keep going and it could also go backwards so this syn graph can go on for as long as you would like okay so depending on the question and depending on the teacher they could make you draw quite a long scene graph but most of the time it's just going to be in this area over here between -360 and 360 degrees so now that you understand what a basic syn graph looks like oh and by the way sometimes if we change the equation of a sin graph this syn graph is the basic y equals to sin x if i put a 2 in the front for example or put a plus two at the end it can it will change the shape so your syn graph might start doing stuff like that but the basic shape is always gonna look like a wave but we'll get to that in later videos but what i want to do now is speak to you about some important concepts such as the period the domain the range and the amplitude the period is how long does it take for that graph to repeat so we can see that the sun graph starts over here and it takes it repeats one full cycle up to that point over there and so it takes 360 degrees to repeat for grade 10 you must just memorize that only in grade 11 do they start changing that and they start squashing the graph up like that but for grade 10 the period is the distance that it takes to repeat one cycle that will always be 360 degrees so just memorize that the word domain is something that you would have encountered when you did other types of graphs such as parabolas exponentials hyperbolas it's simply explaining the x values so this graph that we can see in front of us goes from minus 360 up to 360. so you could say that the domain is an element so you say x is an element going from minus 360 up to 360. the square brackets tell me that the graph touches minus 360 and 360. i know some people prefer this method over here which is absolutely fine as well but then for that method you must just add xer at the end so the period of a syn graph is always 360 but the domain can change depending on the question so in this question it's going to be between -360 and 360. range is the same as domain but it's just the y values so we'll say y is an element now the lowest y value is minus 1 and the highest y value is 1 because remember the y values go in this direction so it will be y as an element going from -1 up to 1. now your amplitude is always going to be this number over here that's in the front of the equation so in this case it's a one but let me explain what amplitude really means a syn graph has a resting position now the resting position is the place where it's not going up or going down like that it's the point in the very middle so it's this part over here so it's like the halfway position now if you have the halfway position then the amplitude is the distance from the halfway position to the highest point now if the halfway position has a y value of zero and the highest point is one then your amplitude is one and so those are four main terms that you need to get used to and in the lessons after this we're going to become more used to the syn graph cause graph and the tan graph