the minimum and maximum values of 5sin^2 A+4 sinAcosA+2 cos^2 A is?

Question

PLs give me a detailed answer and pls tell me how to approach and solve such problems?

Answer 1

y=3sin^2A+2sin2A+2
dy/dA
=
4cos2A+3sin2A
dy/dA=0
==>
A=k*pi/2+arctan(3/4)/2-pi/4
A=k*pi/2-.4636476
now put different amount of k in the first function
and you'l find
for k=2n+1
function has the maximum value of 6
and for k=2n
function has the minimum value of 1

Answer 2

Often the easiest way to solve these problems is iteratively which I have done. Otherwise you would have to differentiate and set to zero - you know the drill.
max= 6 (at 63.43°)
min = 1 (at 153.43°)

Answer 3

OK then type it in a calculator a scientific one this probably wont work then hit equals