Homework SourseIf is the angle between a line through the origin and the p
If ? is the angle between a line through the origin and the positive x-axis then the area (in cm2) of part of a rose petal (a particular curve written in polar coordinates) is given by
A = 9/16(4? ? sin(4?)). If the angle ? is increasing at a rate of 0.4 radians per minute, at what rate is the area changing when ? is pi/3?
A = 9/16(4? ? sin(4?)). If the angle ? is increasing at a rate of 0.4 radians per minute, at what rate is the area changing when ? is pi/3?
Solution
A=(9/16)(4 - sin 4)
dA/d =(9/16)(4 - 4 cos 4) = (9/4)(1- cos4)
By the chain rule dA/dt = (dA/d)*(d/dt)= (9/4)(1- (cos4/3))*(0.4)
Hence dA/dt = (9/4)*(1-cos ((4*3.14159)/3))*0.4 = 1.45
