 Hello and welcome to the session. In this session we will discuss a question which says that suppose a person's resting blood pressure is 130 over 90, if this person's resting heart rate is 60 beats per minute, like the sign function that represents the blood pressure for T seconds, then graph the function what will be the blood pressure when T is equal to 22. Now before starting the solution of this question, we should know how to solve it. And that is periodic phenomena using trigonometric function is of the type y is equal to l of v into x minus c the whole plus k of v into x minus c the whole plus k. 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. Now here we are given that a person's resting blood pressure is 130 over 90. It means that the blood pressure oscillates between maximum of 130 and minimum of 90. Now let P be the blood pressure and T be the time in seconds a periodic function. Now we have to write sign function is the blood pressure P. Now we know that periodic phenomena using trigonometric function is of the type y is equal to l of v into x minus c the whole plus k. So we have to write sign function that represents the blood pressure P and time T. So it will be of the form of v into T minus c the whole plus k represents vertical Gibbs amplitude C represents. And here T also gives us the midline and let us find equation of midline. Now here maximum is 130 and minimum blood pressure is 90. So here midline now here P is representing the blood pressure and midline is at P is equal to minimum values maximum equal to 130 plus 90 perp to which is equal to 110. 110. Now we know that midline y is equal to k and here we have the midline which is at P is equal to 110 it means vertical shift is equal to 110. And now let us find is given by x which is equal to absolute value of maximum whole upon 2 which is equal to absolute value of. Now here maximum value of blood pressure is 130 minus minimum value is 90 upon 2 upon 2 which is equal to absolute value of 20 which is equal to 20. Therefore A is equal to 20. Now let us find period. Now period is given by 2 pi upon absolute value of v now given 1 minute that is thus 1 beat in 1 second therefore or 1 cycle in 1 second that is heartbeat repeats 1 second absolute value of v is equal to 1 which further implies i is equal to absolute value of v and this implies b is equal to plus minus of 2 pi. Here positive or negative value depends on whether we start a cycle with maximum value or minimum value that is when we start a cycle with maximum value then we take positive value with minimum value then we take negative value where here b is equal to now there is no phase shift where c is equal to 0 equal to 2 pi equal to 0. Now putting all these values in this periodic function which is representing the blood pressure p and time t that is 20 sin of v that is 2 pi equal now here c is 0 so it will be 20 sin of 2 pi t plus k that is 110. Now let us graph this periodic function now for making the graph we will take time t is equal to 0 1 2 3 and so on on horizontal axis and blood pressure p is equal to 20 40 16 80 and so on on vertical axis horizontal line that is midline at p is equal to 110. So we have drawn a horizontal line 110 and then we have drawn the maximum minimum values p is equal to 130 90 that is using amplitude is equal to 20 units above midline or midline at this t is equal to 0 and on y axis we get 110 we start from this point keep in mind the graph of sin function while drawing periodic phenomena using sin function 130 that is at y is equal to 130 minimum point y is equal to 90 and then again reaching the midline thus completing the cycle now we will repeat the cycle extending on both sides of the periodic function 20 sin of t plus 110 that what will be the blood pressure when t is equal to 22. Now we can make use of graphic calculators to graph a function when its equation is known so once we find the equation we can graph the periodic function from graphic calculators. Now the following graph will be made for the function p is equal to 20 t plus 110 with the help of graphic calculator we can predict values of t that is x that is y using graphic calculators. Now we have to find p when t is equal to 22 now we can see from graphic calculator that for t is equal to 22 we have p is equal to the blood pressure will be 110 when t is equal to 22 and here this point on the curve is 22 seconds then blood pressure is 110 so this is the sin and that's all for this session hope you all have enjoyed this session.