 Hello and welcome to the session. In this session we are going to discuss the following question and the question says that Draw the graph of the trigonometric function y is equal to minus 3 into sin of 3x minus pi and determine its amplitude and period. Now let us start with the solution of the given question. We are given the trigonometric function that is y is equal to minus 3 into sin of 3x minus pi. First of all let us draw its graph. For this we make table of values. Now in this table in the first column we have written the x values. In the second column we will write the values for the expression 3x minus pi and in the third column we shall write the values of y which is given by minus 3 into sin of 3x minus pi. Now for x is equal to pi by 3 the value of 3x minus pi will be equal to 3 into pi by 3 minus pi and that is equal to pi minus pi which is equal to 0. And for 3x minus pi equal to 0 we get the value of y as minus 3 into sin of 0 which is equal to minus 3 into 0 which is equal to 0. So for x is equal to pi by 3 the value of y is equal to 0. Similarly we shall find all the values of 3x minus pi and y for the corresponding values of x and thus we have for x is equal to pi by 2 the value of y is minus 3. For x is equal to 2 pi by 3 the value of y is 0. For x is equal to 5 pi by 6 y is equal to 3 and for x is equal to pi y is equal to 0. Now let us plot these values so we get the graph of the given trigonometric function. This is the graph of the given trigonometric function y is equal to minus 3 into sin of 3x minus pi. Now from the graph we can find period and amplitude. We know that period is the length of one cycle so here it is given by pi minus pi by 3 and that is equal to 3 pi minus pi whole upon 3 which is equal to 2 pi by 3. So here period is equal to 2 pi by 3 now we shall find its amplitude. We know that amplitude is the distance between maximum height or minimum height and the midline. Now here the maximum height is at y is equal to 3 and the midline is given by y is equal to 0. So amplitude is given by 3 minus 0 that is equal to 3 so amplitude is equal to 3. So this is the required graph of the trigonometric function y is equal to minus 3 into sin of 3x minus pi. And here in this graph the period is equal to 2 pi by 3 and its amplitude is given by 3. This is the required answer. This completes our session. Hope you enjoyed this session.