May 12, 2011 #1 J 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 1,314 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. Cheers, Jeep ---------- Post added at 06:55 ---------- Previous post was at 06:52 ---------- Last edited: May 12, 2011
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. Cheers, Jeep ---------- Post added at 06:55 ---------- Previous post was at 06:52 ----------
May 12, 2011 #2 FvM Super Moderator Staff member Joined Jan 22, 2008 Messages 52,400 Helped 14,748 Reputation 29,778 Reaction score 14,093 Trophy points 1,393 Location Bochum, Germany Activity points 298,003 The problem is about calculating a definite integral ∫sin x - a dx. As a hint: ∫sinx dx = -cos x
May 12, 2011 #3 J 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 1,314 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
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
May 12, 2011 #4 _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 2,909 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)))
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)))