hello grade 10 math students in this video we're going to be looking at trig graphs we'll be focusing on the S graph in this video the sin graph remember to subscribe for more math videos I also do science let's jump right into the video we will be looking at what a sin or sign graph looks like and how to draw it I will also be going over the following terms period amplitude domain and range this is essentially what a basic sin graph looks like you can see the equation says y = sin x or you can say y Theta my X values are in degrees and we go up in steps of 90 so 90 180 270 360 it's these X values that go into the formula over here along the Y AIS we go up in units so units of one for example so what I'll be doing is I'll be taking each of my X values measured in degrees starting with zero put it in the place of X in my equation type it in on my calculator so essentially I'm going to be typing in sin of zero getting an answer sin of 90 getting an answer and so on I will plot those coordinates on the graph let me show you so we do sin of zero and we get zero we then do sin of 90 remember we go up in steps of 90 that's one then we do sin of 180 which is zero then we do sin of 270 which gives me -1 and then last but not least for this graph we do sin of 360 and we get 0 so there's the result from my calculator it essentially gives me the following coordinates which I can plot on the graph so 0 0 the sin graph starts over here the normal basic sin graph 0 0 then 91 over there 180 0 270 -1 [Music] it's easier to do this on grid paper or line paper but you'll see what I mean the shape that's all we care about 360 and Z over there make sure you draw your dots nice and big so that your teacher can see where your coordinates are and then you connect your dots and remember that your trick graphs need to be curvy so your graph needs to look somewhat like this please don't make it look like this with straight lines it's definitely not a straight line graph like that you need to make sure you connect the dots and that there are curves involved in your sign graph mine is not perfect either you can do it a lot neater than I can and then generally we label our T our turning points as well so that's the part of the graph where the graph goes from increasing you can see here it's increasing it's going up to decreasing so up here the peak the maximum that's called the turning point so we label it 90 and 1 we can label this turning point over here 2 70 And1 it's very important to note that the sin graph does not just exist for the parameters that I drawn it over here the S graph is continuous and it extends in both directions infinitely so that pattern repeats itself on and on and on again it's a wave you can see in this version of the S graph I have drawn it from - 360° to positive 360° in the previous one I only did it from 0 to 360° so as I mentioned we plot every 90° on the xaxis remember to draw your graph curvy label your turning points now for domain versus Range you'll be asked the domain or the range for different functions especially trig functions as well like we're doing over here so the domain these are the X values for which the graph exists generally you are given the domain so they give you the domain the X values for which they want the graph drawn and you draw the graph or if they give you a graph that they have drawn for you you can visually see the domain it's all the X values for which that particular graph exists the range is all the Y values for which the graph exists and how I remember the difference is that range has a g a long G and Y you can see what I did over there to help me remember so for this sin graph over here they said that this is the graph yal sin Theta where Theta is an element of 0 to 360 now just remember what this means is that the graph the X values of the graph because domain is X values the graph exists for X values from zero so where X is zero remember X is Z over here all the way to where X is 360° we can see that for this particular sin graph it doesn't go further than 360 and it doesn't go further to the left from zero it doesn't extend into the negatives for the X values so the remain is from zero and the square brackets you need to remember means including zero so the graph starts at zero it exists where X is equal to Z there's a coordinate on zero and it carries on to where X is 360 it exists over there so the square brackets means including and the domain is generally given to you in questions so either they will say draw the graph for the following domain there are basic basally telling you to start drawing on your x-axis from 0 to 360 they don't want any further than that or basically you can look at the graph and determine the domain from the graph so it's all the X Valu so the Starts Here ends there the domain for this graph is from X X is an element of - 360 including - 360 to positive 360 now the range remember are all the Y values so where does the graph exist along the Y AIS if you take a look at this graph over here we can see that the minimum y value is -1 the graph doesn't exist below that yalue yes you can label this as -2 and -3 but the graph doesn't exist down here so the minimum y value is -1 and the maximum y value is positive 1 so the range therefore is y is an element of it's y because range are all the Y values Open brackets square brackets -1 to positive 1 remember you must use square brackets because the square brackets means including it is including negative 1 and and it is including one the period is how long it takes for one full cycle or one wave to complete so look at the sign graph over here we start at zero we go to a maximum back to zero to a minimum back to zero that represents one full cycle one full wave to complete that is 360° so the period for a normal sin graph yal sin of theta the period period is equal to 360° okay let's take a look at this graph over here that I drew for you earlier if you take a look at what's happening here you can clearly see that's one side cycle and that's one cycle so there's two full Cycles on the graph but remember the period is how long it takes for one full cycle so if you look at the green graph from - 360 to 0 that's 360° so the period is 360° in grade 10 for sin graphs your period will always be 360 this does change when you do trig graphs in grade 11 and grade 12 but for grade 10 always going to be 360 you can think of the amplitude as the distance from the resting position also can be called the equilibrium position it's kind of the middle position or the halfway mark over here I'm highlighting it in yellow so it's basically here you can see the graph is increasing here you can see the graph is decreasing it's kind of like in the middle of those two so it's the distance from this resting position to the highest point and how many units is that one unit so the amplitude in this case is is one you can also think of it as the number in front of sin so this is the equation for the following graph over here the number in front of sin is one it's invisible but there's a one in front of sin we can change the amplitude so in later videos I'll show you what it looks like if we change it to two Y = 2 sinx basically it'll cause a vertical stretch so instead of the graph ending here the graph will go up to two so say this is two the graph will go like that I hope that makes sense and it'll go down to -2 so it stretches the graph we can also calculate the amplitude so how you do that is you take the maximum y value so that would be 1 so the amplitude is the maximum yalue 1 minus the minimum yvalue so minus and the minimum is -1 so minus -1 and we divide it by 2 so at the top I have 2 1 - - 1 is 2 2 / 2 the amplitude is 1 take note if the amplitude is negative it means that the graph has been reflected in the x axis remember this is the x axis so if you have a reflection in the x axis something that was here will now be here so take a look at the normal sin graph y = sin x the amplitude is one the number in front of sin is one that looks like the normal graph that we plotted earlier but if a is negative 1 see how there's a negative you can see that the graph has been flipped around in the x axis so here we go from z0 to positive 1 back to zero here we go from 0 to1 back to zero here is a summary of the basic sin graph the domain the range period and amplitude now remember the domain it depends on what they give you in the question we could could have a domain that for example goes from 90 to positive 360 it just really depends on what is given to you so that can change that's why it's got a blue star next to it it changes depending on the formula or the question the range is the Y values again that can change depending on the formula and the amplitude amplitude can also change but the period is always 360° in the next video we'll be going over the ca graph I can't wait to see you then bye everyone and