hello everyone and welcome to another video in this lesson we are going to talk about the tan graph okay now with the tan graph you typically going to use steps of 45 degrees and not one i mean not 90 degrees because you know in the previous lessons we used 90 degrees for each of our steps okay i've run out of space a bit here so i'm just going to extend this 315 and 360. then i'm going to do the reverse and then the y values you can typically just still use 1 and minus 1. that's not really a big issue here so then once again we're going to call on our calculator and we're going to just type in the values so for example i'm not going to show you the calculator this time i'm sure you guys understand by now so we start off at 0 degrees which is over here so you type in tan 0 on your calculator and you'll see that the answer will be zero so we'll just put a dot right there then you type in tan 45 and you calculate and it's going to give you a one so you put it over there then an interesting thing about tan is that if you type in tan 90 you're going to get an error on your calculator that just means that you should draw a dotted line going down the 90 degree part like that then we carry on tan of 135 that should give you negative 1 so that's over here tan 180 is 0 10 225 is one the tan of 270 gives us another error and then the tan of 315 is minus 1 and then the tan of 360 is zero then i'm just going to do the reverse side tan of negative 5 is minus one tan of minus ninety is another error so you just draw dotted lines tan of minus one thirty-five gives us a positive one tan minus one eighty ten minus two two five gives us negative 1 10 negative 270 gives us another error tan of minus 3 1 5 gives us 1 and then 10 minus 360 gives us 0. now we've got to connect this so the way it works is you start off at the zero position and you just want to go as close to these dotted lines as possible and then you just go up like that so down here you want to be as close to the dotted line as possible and up here you want to be as close to the dotted line as possible and then you just connect the dots like that and then over here we can connect the dots so it goes along that one here you just connect the dots and so it will go down there see if i just connect the dots then naturally i can see which direction it goes in and then this one will just go up here and then if i just connect the dots and then it goes there so you just want to let these like little snakes i guess they you just need to get them as close to the dotted lines as possible but don't let them cross over so we can see all over we've got these dotted lines and that's it that's a tan graph now we need to talk about amplitude period all of that stuff okay so the period now remember for sin and cause i said that you should memorize 360 well for tan you're also going to memorize but you're going to memorize 180 for the amplitude now remember amplitude on a syn graph for example we said that you should find the resting position which was over here and then you should measure the distance to the highest point problem is with the sun i mean a tan graph is that it doesn't have a highest point these arrows are trying to tell us that this thing just keeps going up up up up or it keeps going down down down so the amplitude does not exist so we can just say n a not applicable the domain well that's just what they've given you so they've clearly given us from minus 360 up to 360. so you'll just say xe going from -360 up to 360. oh but what's very important i nearly forgot is that the graph does not exist at 90 270 minus 90 minus 270. so the way that you would show that is next to this part over here you would have to say something like x cannot be and then you'd list all those values so minus 270 minus 90 90 and 270 x can't be those values that's why we've put a line through it like that so you're saying that x is all the numbers from -360 up to 360 but it can't be those values over there then the range well check this out the lowest value of this graph it just keeps going and then the highest value of this graph just keeps going so you could say that y is an element going from minus infinity all the way to positive infinity and remember with infinity you don't use a square bracket you always use a round bracket