 Hello and welcome to the session. In this session we will discuss a question which says that state the vertical shift amplitude period and phase shift of the graph of the periodic function y is equal to 3 sin of 2 of theta plus 30 degrees the whole plus 10. Now before starting the solution of this question we should know a result and that is general form of sin function is y is equal to a sin of b of x minus 3 by del plus k where amplitude k represents vertical shift and c represents phase shift here period is equal to 3 pi upon modus of b. Now this result will work out as a key idea for solving out the given question. Now let us start with the solution of the given question where v is equal to a periodic function y is equal to 3 sin of 2 of theta plus 30 degrees the whole plus 10. Now for the key idea we know the general form of sin function so on comparing this periodic function with the general form of sin function we have a is equal to 3 b is equal to 2 and v is equal to 10 and c is equal to minus 30 degrees because this 30 degrees can be written as theta minus of minus 30 degrees and comparing it with the general form of sin function we have b is equal to minus 30 degrees. Now is equal to absolute value of a this is equal to now a is equal to 3 and absolute value of 3 is equal to now we know that period is equal to 2 pi upon absolute value of b now b is equal to 2 so this is equal to 2 pi upon absolute value of 2 this is equal to 2 pi upon 2 and this is equal to pi is equal to now from the key idea we know that k represents the vertical shift k is equal to 10 so as k is equal to 10 therefore vertical shift is equal to 10 and since it is positive it means shifted upwards now here so here midline is drawn at y is equal to 10 and where c is equal to minus 30 degrees is equal to minus 30 degrees that is c is equal to minus 30 degrees 30 degrees can be written as minus pi by 6 is less than 0 thus by pi by 6 of the given periodic function period is equal to pi is equal to minus over the session hope you all have enjoyed the session.