sinX=cosY有什么结论？
sinx=cosy=sin(π/2-y)x=2kπ+π/2-y，得x+y=互余+周期
或x=2kπ+π-π/2+y=2kπ+π/2+y，得x-y=90+周期
绛旓細sinx=cosy=sin(蟺/2-y)x=2k蟺+蟺/2-y锛屽緱x+y=浜掍綑+鍛ㄦ湡 鎴杧=2k蟺+蟺-蟺/2+y=2k蟺+蟺/2+y锛屽緱x-y=90+鍛ㄦ湡
绛旓細sinx绛変簬cosy鎰忓懗鐫x鍦焬=蟺/2+2k蟺锛宬鈭圸銆傚洜涓篶osy鍙互鍐欐垚sin(蟺/2-y)锛屽洜姝ゆ湁sinx=sin(蟺/2涓y)锛屼袱涓笉鍚岀殑瑙掓寮︾浉绛夛紝杩欎袱鍙鍙互鐩稿樊2k蟺锛屾垨鑰2k蟺鍗佅涓鏌愯锛屽嵆鏈墄=2k蟺鍗佅/2涓y锛屾垨x=2k蟺鍗佅-(蟺/2涓y)銆傚氨鏄痻鍗亂=2k蟺鍗佅/2鎴杧涓y=2k蟺鍗佅/2锛宬鈭圸銆
绛旓細鈭cosy=cos(蟺-x)= - cosx 鑰- cosx鈮sinx 鈭存槸鍋囧懡棰 鏂规硶浜 锛氬彲浠ュ甫鍏ョ壒娈婂 sin4/蟺=cos4/蟺 4/蟺+4/蟺=2/蟺 鑰屼笉鏄 鎵浠ユ槸鍋囧懡棰
绛旓細涓婇潰鐨勭瓟妗堥兘涓嶅畬鏁.鍙互杩欐牱鍖栦竴涓:sinx=sin(90搴-y+360搴*n)鎴=sin(90搴+y+360搴*n), (鍏朵腑n涓烘暣鏁).鎵浠鍜寉鐨勫叧绯讳负:x+(鎴-)y=90搴+360搴*n (鍏朵腑n涓轰换鎰忔暣鏁)
绛旓細濡傛灉璇磋冭檻cosx鍑芥暟鐨勫懆鏈熸х殑璇濓紝杩欎釜涓嶈兘绠楁槸鐪熷懡棰橈紝鍙兘璇存槸璁╃瓑寮忔垚绔嬬殑涓绉嶆儏鍐碉細sinx = cos(蟺/2 - x)cos(蟺/2 - x) = cos(y)浣犲啀鍒嗘瀽(蟺/2 - x)涓巠涔嬮棿鐨勫叧绯诲氨鐭ラ亾浜
绛旓細0<=y<=1骞朵笖x^2+y^2=1.鑰屽鏋滈渶瑕 sinx=cosy,閭ｄ箞灏遍渶瑕: (Pi鏄渾鍛ㄧ巼)x+y=2k*Pi+Pi/2,鎴栬 x-y=2k*Pi+Pi/2.鑰岃繖浜涙暟涓,鎴戜滑鍙渶瑕佷緷鎹 |x-y|>=Pi/2,灏卞緱鍒:|x^2+y^2|>1,鍐嶆牴鎹畖x+y|>=Pi/2,涔熷緱鍒:|x^2+y^2|>1,鎵浠ユ病鏈夊悓鏃舵弧瓒宠繖涓や釜鏉′欢鐨!
绛旓細鎴栬呰锛屾湁鏃犵┓澶氱粍瑙ｏ紒鑰冭檻鍒版槸涓夎鍑芥暟锛屽洜涓sinx=cosy锛屾墍浠+y=蟺/2锛屽嵆锛歽=蟺/2-x 鍗筹細sinx=cosy sinx=cos(蟺/2-x)sinx=sinx 鍥犱负0鈮鈮は/2锛岃寈鍙互鏄0鍒跋/2鐨勪换鎰忚搴︼紝鑰寉=蟺/2-x銆傚鏋滄槸sinx=cosx鐨勮瘽锛岃繕鏈夊彲鑳斤紒x=蟺/4 鍋氭硶鏄細sinx=cosx sinx=鈭歔1-(sinx)^2](...
绛旓細x+y=90+360n锛宯灞炰簬鏁存暟
绛旓細sinxcosy绛変簬(1/2)sin2x銆備笁瑙掑嚱鏁版槸鏁板涓睘浜庡垵绛夊嚱鏁颁腑鐨勮秴瓒婂嚱鏁扮殑鍑芥暟銆傚畠浠殑鏈川鏄换浣曡鐨勯泦鍚堜笌涓涓瘮鍊肩殑闆嗗悎鐨勫彉閲忎箣闂寸殑鏄犲皠銆傞氬父鐨勪笁瑙掑嚱鏁版槸鍦ㄥ钩闈㈢洿瑙掑潗鏍囩郴涓畾涔夌殑銆傚叾瀹氫箟鍩熶负鏁翠釜瀹炴暟鍩熴傚彟涓绉嶅畾涔夋槸鍦ㄧ洿瑙掍笁瑙掑舰涓紝浣嗗苟涓嶅畬鍏ㄣ傜幇浠ｆ暟瀛︽妸瀹冧滑鎻忚堪鎴愭棤绌锋暟鍒楃殑鏋侀檺鍜屽井鍒嗘柟绋嬬殑瑙...
绛旓細鎴戣寰梩an x=sin x锛廲os x鍙互鐞嗚В涓烘槸浜哄畾涔夌殑.涓嶅瓨鍦ㄤ负浠涔.sin 鏄杈规瘮鏂滆竟 cos鏄复杈规瘮鏂滆竟 tan鏄杈规瘮涓磋竟 銆傛墍浠ユ湁杩欏叕寮 銆傜浜岄鍙互鐢ㄥ崟浣嶅渾鐨勬柟娉曘傛垨鑰呯敤cos(90-x)=cos90cosx+sin90sinx=sinx 鍙﹀涓や釜绫讳技
