00:01
In this question, we need to sketch the following graph by the following transformation, which are given here.
00:06
Okay, step by step, we are going to solve this question because this is very good question.
00:12
And here, one thing you should notice, that x is in between 0 to 2 pi.
00:17
Okay.
00:18
So the first step is the basic graph of sine of x, how it looks like.
00:24
Okay, so let us see.
00:26
So we know that in 0 to 2 pi, sine x graph is somewhat of, this sort okay so this is zero pi and this is two pi okay so this is nothing but sine of x now we will draw what is sine of three x so each entry will get divided by three okay so in this case our graph will be somewhat of this same you see here now sine of three x means what pi becomes pi divided by three instead this becomes two pi divided by three okay means what every this term okay pi and two pi they all will get divided by three okay so what i will get here there will be somewhat of this same okay because you see we know the range is negative one to positive one so this is zero initially this was pi so now this time it will be pi divided by three so this becomes what two pi divided by 3 and this becomes pi okay so if you go on you will get this to be equal to 2 pi okay now the next thing is to draw the graph of sign of 3x plus 3 pi okay so that means what sift the graph leftward by pi okay so safe graph left by pi okay because if you solve 3x plus 3x plus pi equal to zero so this will give you xe equals to minus pi so minus pi indicates shift towards left okay so in this case let's see how our graph is going to look like so the graph will look like somewhat of the same in this case you see our graph will be of this same okay so this will be my graph in this case and after shifting left toward by pi units so this becomes pi divided by three okay and this becomes my pi and so on this becomes two pi okay now minus half also we need to add in this so finally i will draw the graph of sign of three x plus three pi minus half so it will be sift downward by minus half okay so shift downward by half unit okay so in this case let us see how our graph look like so in this case if i draw the graph that we draw here okay so again the graph will be somewhat of this you see it will be shifted well already it is at minus one so if you sent half unit downward further it will be minus one plus minus one minus half that is minus 3 divided by 2 so it will be here somewhere minus 3 divided by 2 and here it was 1 shift half downward so it becomes 1 divided by 2 okay 1 divided by 2 now you can draw the graph here so it will be somewhat of this thing okay so this is how a my graph will look like okay so you see now sorry a graph is not correct here because it is minus half graph will start from here okay so it will be going up till here then here and like this my graph will be okay and it will again end with this so this is my two pi okay so corresponding to this is the two pi and corresponding to this part here okay it is pi okay it is pi okay and somewhere here, i will get pi divided by three.
04:53
And this is pie.
04:53
So this is my final graph.
04:55
So this is how we can solve this question.
04:58
Okay.
04:58
So this is the final graph.
05:03
Okay.
05:04
Now let us go for the second graph...