Question

Consider Figure 1 below. The cross-sectional area A of a gutter with equal base and edge length of 2 is given byA = 4sinθ (1+ cosθ )

Find the angle θ which maximizes the cross-sectional area of the gutter. Using an initial interval of [0,π / 2], find the solution after 2 iterations. Use an initia lε = 0.05 . Golden Search Method 09.01.12

Figure 1 Cross section of the gutter

Answer 1

As given,

Now we calculate initial intermediate points

and,

Calculating function value

Since ,

Now , for rejection checking

Iteration 2:

Now we calculate initial intermediate points

and,

Calculating function value

Since ,

Now , for rejection checking

So aprrox solution is