Thread: Area and limit of the shaded region...?

I'm not sure if I did this is right, but here's the question:

Consider the shaded region outside the sector of a circle of radius 10 meters and inside a right triangle.

a) write the area A= f(θ) of the region as a function of θ.

My equation: f(θ) = 50θ - 50 arctanθ

b) What is the domain of the function?

All real numbers.

c) Find lim (θ--> π/2-) A.

Infinity... why?

Thanks!

Originally Posted by damselfly

a) write the area A= f(θ) of the region as a function of θ.

My equation: f(θ) = 50θ - 50 arctanθ

Not quite. The area of the triangle is , from which you substract the area of the piece of disc ( , indeed), so that .

Now you can reconsider the other questions.

Laurent.

Hello, damselfly!

Consider the shaded region outside the sector of a circle of radius 10 meters
and inside a right triangle.

Code:

    B *
      |:*  D
      |:::*
    h |:*   *
      |*      *
      |      θ  *
    C * - - - - - * A
           10

a) Write the area of the region as a function of

In right triangle

Area of

Area of sector

Therefore: .

b) What is the domain of the function?

could be any acute angle from 0° to less than 90°.

. . .

c) Find: .

Answer: Infinity . . . why?

As increases to , the radius becomes vertical.

Code:

      |:::::::::|
      |:::::::::|
      |:::::::::|
      |:::::::* * D
      |:::*     |
      |:*       |
      |*        |
      |       θ |
    C * - - - - * A
           10

And the area of the "triangle" becomes infinite.

Thank you so much!