A rectangle is inscribed in a semicircle of radius 1.

(a) Express the area A of the rectangle as a function of the angle theta.

(b) Show that A = sin(2theta)

Printable View

- August 29th 2008, 12:04 PMmagentaritaRectangle Inscribed in Semicircle...Part 1
A rectangle is inscribed in a semicircle of radius 1.

(a) Express the area A of the rectangle as a function of the angle theta.

(b) Show that A = sin(2theta) - August 29th 2008, 02:27 PMJhevon
um, what angle is theta?

in any case, i think it would be a good idea for you do draw this on a pair of axis. let the rectangle sit on the x-axis with its top vertices touching the upper-half circle of radius 1 centered at the origin. try to center the rectangle also. see if that gives you any ideas - August 29th 2008, 02:32 PMSoroban
Hello, magentarita!

Quote:

A rectangle is inscribed in a semicircle of radius 1.

(a) Express the area of the rectangle as a function of

(b) Show that: .

Code:`* * *`

* | *

*-------+-------*

*| | * |*

| | 1* |y

* | | * θ | *

*-+-------+-------+-*

x

The area of the rectangle is: .

We have: .

Therefore: .

- August 29th 2008, 06:30 PMmagentarita