stupid trig question (1 Viewer)

[taco man]

hi can sum 1 do this for me...i've got part 1 right but i'm getting sumthing diff for part 2:

the angle x between two radii OP and OP of a circle of radius 6cm is increasing at the rate of 0.1 radians per minute

a)show that area of sector OPQ is increasing at the rate of 1.8cm^2/min
b)find the area at which the area of triangle OPQ is increasing at the instant when x is equal to pi/4

thanks

 

[Libbster]

For part A,

we know that dx/dt = 0.1
we know that the area of a sector = 1/2r^2x
Thus, when r=6 A=18x
Thus, dA/dx= 18
since we are looking for dA/dt using the chain rule

dA/dt = dx/dt . dA/dx
dA/dt = 0.1 x 18
= 1.8