Find the rate of P=0.5A(sqare) cos2A, at the point where A=1.8

Question

Find the rate of P=0.5A(sqare) cos2A, at the point where A=1.8

Answer 1

If I understand your typing,  I'm assuming the following:

P = (0.5)A² COS(2A) 

 

For rate, we take the derivative, then plug in value A = 1.8

 

For the derivative  

DP/DA = D/DA [0.5 A²] *COS(2A)  + 0.5A² D/DA [COS(2A)]

 

DP/DA = 2*0.5 A * COS(2A) + 0.5 A² [-SIN(2A)*2]

 

DP/DA = A*COS(2A) -  A² SIN(2A)         ! Note in both terms, the 0.5*2 = 1

 

PLUGGING IN A = 1.8    

 

DP/DA = 1.8*COS(3.6) - 1.8² SIN(3.6)           (Make sure angle is in Radians mode in Calculator)

 

DP(1.8)/DA = -0.18