Find the maximum and minimum values of the function g ( θ ) = 5 θ − 6 sin ( θ ) on the interval [ 0 , π /2 ]

Minimum value of the given function is  0

Maximum value of the given function

Step-by-step explanation:

Step(i):-

Given function    g ( θ ) = 5 θ − 6 sin ( θ )  ...(i)

Differentiating equation (i) with respective to 'θ'

                            g¹ ( θ ) = 5  − 6 cos ( θ ) ...(ii)

                          g¹ ( θ ) = 5  − 6 cos ( θ ) =0

                          5 = 6 cos ( θ )

                       cos ( θ ) = 5 /6  

Step(ii):-                        

Again Differentiating equation (ii) with respective to 'θ'

                              g¹¹ ( θ ) =   − 6 (-sinθ )  = 6sinθ

Given interval

                         θ = 0 and   θ= π/2

                     g ( 0 ) = 5 (0) − 6 sin ( 0 ) = 0

                     g(π/2) = 5(π/2) - 6 sin (π/2)

                               =  5(π/2) - 6

                               =

answer

a,b, and d

explanation

a reflection angle is more than

but less than;

an angle that measures

is a reflex angle.(true)

an angle that measures less than

is acute.(true)

provided we are considering angles greater or equal to zero.

an acute angle lies in the range.

an obtuse angle is less than 180° but more than 90°

an angle that measures 300° is obtuse (false)

an angle that measures 65° is an acute angle.(true)