# Thread: Max/Min Problems with Trig.

1. ## Max/Min Problems with Trig.

Hi

Could someone please give me hints 4 the questions circled in the attachment? I have no clue how to start to arrive at those answers.

Thanx a lot.

2. Hello xwrathbringerx
Originally Posted by xwrathbringerx
Hi

Could someone please give me hints 4 the questions circled in the attachment? I have no clue how to start to arrive at those answers.

Thanx a lot.
1(a) Let $\displaystyle QR = x$. Then $\displaystyle QP = x\cos\alpha$.

So $\displaystyle x(1+\cos\alpha) = 2$ (= total length of wire)

And $\displaystyle PR = x\sin\alpha$

Then use $\displaystyle A = \tfrac12.PR.QP$

2(a) Draw vertical lines through the top vertices of the trapezium to the base. Then using the right-angled triangles thus formed, the width of the channel across the top is $\displaystyle 4+ 4\cos\theta + 4\cos\theta = 4 + 8\cos\theta$, and the depth of the channel $\displaystyle = 4\sin\theta$.

Then use the formula:

Area of a trapezium =$\displaystyle \tfrac12$(sum of parallel sides) $\displaystyle \times$ (perpendicular distance between them)

$\displaystyle =\tfrac12(4 + 4 + 8\cos\theta)\times 4\sin\theta$

$\displaystyle = ...$