Welcome to EDAboard.com

Welcome to our site! EDAboard.com is an international Electronic Discussion Forum focused on EDA software, circuits, schematics, books, theory, papers, asic, pld, 8051, DSP, Network, RF, Analog Design, PCB, Service Manuals... and a whole lot more! To participate you need to register. Registration is free. Click here to register now.

Sine wave segment area computation

Status
Not open for further replies.

jeep brainy

Newbie level 4
Joined
Oct 30, 2009
Messages
6
Helped
0
Reputation
0
Reaction score
0
Trophy points
1,281
Location
ireland
Activity points
1,313
Hi Everyone,
I need to derive a formula for computing an area of a segment within a sine wave.

Given the length of chord (X) and wavelength (Z), how would I get the area of segment A. Many thanks in advance for any help.

Presentation1-2.png


Cheers,
Jeep

---------- Post added at 06:55 ---------- Previous post was at 06:52 ----------
 
Last edited:

FvM

Super Moderator
Staff member
Joined
Jan 22, 2008
Messages
48,211
Helped
14,207
Reputation
28,673
Reaction score
12,903
Trophy points
1,393
Location
Bochum, Germany
Activity points
279,282
The problem is about calculating a definite integral ∫sin x - a dx. As a hint: ∫sinx dx = -cos x
 

jeep brainy

Newbie level 4
Joined
Oct 30, 2009
Messages
6
Helped
0
Reputation
0
Reaction score
0
Trophy points
1,281
Location
ireland
Activity points
1,313
Hi FvM,
Thanks for your reply but could you further explain.
Please note on those to variables (x and z), I want to compute for the area using them.

cheers,
jeep
 

_Eduardo_

Full Member level 5
Joined
Aug 31, 2009
Messages
295
Helped
118
Reputation
238
Reaction score
103
Trophy points
1,323
Location
Argentina
Activity points
2,843
The limit angle is: θo = acos(x/(2z))

Then the whole grey area:
A = 4 ∫(cos(x) - cos(θo))dx ; 0,θo

A = 4 (sin(x) - x cos(θo)) |0,θo = 4 ( sin(θo) - θo cos(θo))

A = 4 ( √(1-(x/(2z))²) - (x/(2z)) acos(x/(2z)))
 

Status
Not open for further replies.

Part and Inventory Search

Welcome to EDABoard.com

Sponsor

Top