Could someone please help me figure out how to optimize this equation?

An electric current, I, in amps, is given by:





I = cos(w*t) + (鈭?)*sin(w*t),





where w 鈮?0 is a constant. What are the maximum and minimum values of I?Could someone please help me figure out how to optimize this equation?
I = cos(蠅t) + (鈭?)sin(蠅t)





Take the derivative:


I' = -蠅sin(蠅t) + (鈭?)蠅cos(蠅t)





Set the derivative equal to zero:


-蠅sin(蠅t) + (鈭?)蠅cos(蠅t) = 0


Divide both sides by 蠅:


-sin(蠅t) + (鈭?)cos(蠅t) = 0


Add sin(蠅t) to both sides:


(鈭?)cos(蠅t) = sin(蠅t)


Divide both sides by cos(蠅t):


sin(蠅t)/cos(蠅t) = 鈭?


tan(蠅t) = 鈭?


蠅t = arctan(鈭?)


t = arctan(鈭?)/蠅





You'll probably need a calculator from here, but I think you can handle it now. Don't forget to use the 2nd derivative test in order to see if the critical points you find are maximums or minimums.Could someone please help me figure out how to optimize this equation?
k well that's what you were supposed to do Report Abuse

freckles