Question

If an appliance is plugged into a common household​ outlet, the wattage consumed is not constant.​ Instead, it varies at a high frequency according to the model Upper W equals StartFraction Upper V squared Over Upper R EndFraction equals StartFraction left parenthesis 163 sine 120 pi t right parenthesis squared Over 95 EndFraction ​, where V is the voltage and R is a constant that measures the resistance of the appliance. Use the identity cosine left parenthesis 2 theta right parenthesis equals 1 minus 2 sine squared theta to determine values of​ a, c, and omega so that Upper W equals a cosine left parenthesis omega t right parenthesis plus c. Check your answer by graphing both expressions for W on the same coordinate axes. Find the equation for​ W, using the values of​ a, c, and omega. aequals nothing ​(Type an integer or decimal rounded to the nearest tenth as​ needed.) cequals nothing ​(Type an integer or decimal rounded to the nearest tenth as​ needed.) omegaequals nothing ​(Type an exact answer in terms of pi​.)

Answer 1

given appliance lugged into power supplly
   given wattage model
   W = V^2/R = [163*sin(120*pi*t)]^2/95
   comparing
   V = 163*sin(120*pi*t)
   and
   R = 95 ohms

   identity
   cos(2*theta) = 1 - 2*sin^2(theta)

   hence
   W = [163*sin(120*pi*t)]^2/95 = 279.673684*sin^2(120*pi*t) = 139.836842105263(1 - cos(240*pi*t))
   W = a*cos(wt) + c
   comapring
   a = -139.83684
   w = 240*pi
   c = 139.83

   the graphs for two equations is as under
   W = V^2/R = [163*sin(120*pi*t)]^2/95