Derivative optimization trig functions, give it a try please grade 11 math

[livelaughlove]

could someone please try and solve this? and explanation would be greatly appreciated too !
this was one of the homework questions, but i didnt really understand. the teacher explained it again to the class partly, but didnt understand a part of it so we didnt continue...

maybe one of you guys could do it? its grade 11 (IB) math , and Its derivative optimization of trig functions
i uploaded the question (thers a schema with the question too)

http://photos-h.ak.fbcdn.net/hphotos-ak-snc3/hs145.snc3/17245_418921415214_614755214_10740817_1385551_n.jpg reply asap ! :P thankss !

 

[livelaughlove]

oups. k ill put it in homework section cause they want me to.

 

[HallsofIvy]

The area of an entire circle is, of course, $\pi r^2$. A "circular sector", with central angle $\theta$ (in radians) is $\theta/2\pi$ of the entire circle so the area of such a sector is $\pi r^2\theta/2\pi= r^2\theta/2$.

The rest of the figure is two triangles and a rectangle. To find their areas, you need to know "width" and "height". The two right triangles each have hypotenuse of length 10 and angle $\pi/2- \theta$. You can find the lengths of their legs with sine and cosine. Of course, the height and width of the rectangle is given by the lengths of the legs of the right triangle.

 

[cjwalle]

Okay, let's break it down into several manageable pieces.
It consists of:
The sector BOC
2 equally sized triangles (I'll call them COD and BOE, hope you understand my referencing)
The triangle DOE

Try adding those areas together.

As for maximising it, the procedure I'm sure you've seen in the book is deriving it and putting it = 0. Let me know if you don't get it, and I'll help out further :)

 

[livelaughlove]

great guys ! oomg thankkk youu soo muchh i get it now :D i think lol

wow, thank you :)

 

[Prologue]

Small correction. The angle for the triangles will satisfy this equation

$$2\phi+\theta=\pi$$

Where phi is the angle on either side of theta, but within each triangle. Solve for phi to get

$$\phi=\frac{\pi}{2}-\frac{\theta}{2}$$

 

[livelaughlove]

yep, already got it though! :)
thanks