双纽线极坐标方程r∧2=cos2θ,cos2θ的值域是-1到1,r的取值范围明显不是-1到1 极坐标方程r^2=cos2θ是双纽线，我觉得周期应该为pi，...
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绛旓細r鐨勫彇鍊艰寖鍥存槸[0,1]鍚э紝鍥犱负r²=cos2胃鈮1锛岃鏋佸潗鏍囨柟绋鍙堣姹俽鈮0
绛旓細瀹冩槸鏈夊懆鏈熺殑鍟婏紝浣嗘槸骞朵笉鏄笁瑙鍧愭爣閭ｇ鍛ㄦ湡锛岃繖鏄叧浜庡埌鍘熺偣璺濈鍙樺寲鐨勫懆鏈熴備綘鍦ㄨ鍥惧儚涓婁换鍙栦竴鐐癸紝鐒跺悗閫嗘椂閽堟棆杞180掳锛屼綘鐪嬬湅鏄笉鏄埌鍘熺偣璺濈杩樻槸涓鏍风殑鍢涳紵杩欏氨鏄懆鏈熴
绛旓細蟻^2=cos2胃鐨勫浘鍍忔槸鍙岀航绾銆傝В锛氭湰棰樺埄鐢ㄤ簡鍗¤タ灏煎嵉褰㈢嚎鍜屾寮﹁灪绾跨瓑鏇茬嚎鐨勭壒娈婃ц川姹傝В銆侾^2=cos2胃鏄鏋佸潗鏍涓航鎵ｆ洸绾跨殑鏂圭▼ 銆傛眰瑙ｆ柟娉曚负鎶婂畠鍖栦负鐩磋鍧愭爣绯伙細r^4=(cos^2胃-sin^2胃)r^2 (x^2+y^2)^2=x^2-y^2 鍗 x^4+y^4+2(x^2y^2)-x^2+y^2=0銆傚張鍥犱负x锛寉姝ｈ礋鐨...
绛旓細鍙岀航绾挎瀬鍧愭爣鏂圭▼瑙掑害胃鑼冨洿鏄粠0鍒跋/4銆傚弻绾界嚎鏋佸潗鏍囨柟绋嬫槸蟻^2=2a^2*cos2胃銆傚弻绾界嚎锛屼篃绉颁集鍔埄鍙岀航绾匡紝璁惧畾绾挎AB闀垮害涓2a锛岃嫢鍔ㄧ偣M婊¤冻MA*MB=a^2锛岄偅涔圡鐨勮建杩圭О涓哄弻绾界嚎銆傚弻绾界嚎鏄崱瑗垮凹鍗靛舰绾垮拰姝ｅ鸡铻虹嚎绛夋洸绾跨殑鐗规畩鎯呭喌銆傚弻绾界嚎鍙氳繃绛夎酱鍙屾洸绾跨粡杩囧弽婕斿緱鍒帮紝鍗冲畠鏄弻鏇茬嚎鍏充簬鍦嗗績...
绛旓細1. 鍙岀航绾鐨鏋佸潗鏍囨柟绋涓:ρ^2=a^2*cos2θ銆2. 瑕佽浆鍖栦负鍙傛暟鏂圭▼锛屽彲浠ヨ繖鏍峰鐞:鏍规嵁X= ρ cos θ锛 y= ρ sin θ锛屽彇ρ= a√cos2 θ锛岄氳繃浠ｅ叆寰楀埌鍙傛暟鏂圭▼:X= a√(cos2 θ) cos θ锛 y=a√(cos2 θ) ...
绛旓細杩欏氨鏄 鍙岀航绾鐩磋鍧愭爣鏂圭▼銆傚湪鏋佸潗鏍囦腑锛屽彲鍖栫畝寰椣乛2=2a^2*cos2胃 鍙︿竴涓弻绾界嚎鐨勬柟绋嬫槸锛毾乛2=a^2*sin2胃 鏋佸潗鏍囨柟绋涓嬶細x=蟻cos胃,y=蟻sin胃 瀵兼暟鏂圭▼ 蟻^2=a^2*cos2胃鐨勫鏁版柟绋嬶細蟻=-1*sin(2胃)*cos(2胃)^(-0.5)蟻^2=a^2*sin2胃鐨勫鏁版柟绋嬶細蟻=sin(2胃)^(-0...
绛旓細鍙岄挳绾(x^2+y^2)^2=2a^2(x^2-y^2) 锛岀敱蟻鈭2=x鈭2+y鈭2锛寈=蟻cos胃锛寉=蟻sin胃鍖栫畝寰楋紝浠ｅ叆鐩磋鍧愭爣鏂圭▼鏈壪佲埀4=2a鈭2*蟻鈭2(cos鈭2胃-sin鈭2胃)锛岀敱浜屽嶈鍏紡灏辨帹瀵煎嚭鏉ャ傝В锛氬皢蟻锛2cos胃绛夊彿涓よ竟鍚屾椂涔樹互蟻锛屽緱鍒帮細蟻2锛2蟻cos胃銆傛妸蟻2鐢▁2锛媦2浠ｆ浛锛屾妸蟻cos胃鐢...
绛旓細蟻^2=2a^2*cos2胃 鍙︿竴涓鍙岀航绾鐨勬柟绋嬫槸锛毾乛2=a^2*sin2胃 鏋佸潗鏍囨柟绋涓嬶細x=蟻cos胃,y=蟻sin胃 瀵兼暟鏂圭▼ 蟻^2=a^2*cos2胃鐨勫鏁版柟绋嬶細蟻=-1*sin(2胃)*cos(2胃)^(-0.5)蟻^2=a^2*sin2胃鐨勫鏁版柟绋嬶細蟻=sin(2胃)^(-0.5)*cos(2胃)鍙岀航绾垮彲閫氳繃绛夎酱鍙屾洸绾跨粡杩囧弽婕...
绛旓細鍙岀航绾挎瀬鍧愭爣鏂圭▼:(x^2+y^2)^2=2a^2(x^2-y^2)銆備竴銆
绛旓細鍙岀航绾鐨鏋佸潗鏍囨柟绋涓r²=a²cos2t锛宼鈭圼-蟺/4,蟺/4]鈭猍3蟺/4, 5蟺/4]鐢卞浘褰㈢殑瀵圭О鎬т互鍙婂叕寮廠=0.5鈭 r²(t)dt 鍙緱闈㈢НS=4* 0.5* 鈭玔0,蟺/4] a²cos2t dt =a² sin2t| [0,蟺/4]=a²涓嶆槑鐧藉彲浠ヨ拷闂紝濡傛灉鏈夊府鍔╋紝璇烽変负婊℃剰鍥炵瓟锛
