极坐标的半径r可以是负的吗？ 这个用极坐标怎么表示半径
\u9ad8\u4e2d\u6570\u5b66\u4e2d\u6781\u5750\u6807\u4e2d\u7684ℓ\u53ef\u4ee5\u662f\u8d1f\u6570\u5417\uff1f^^^o\u6781\u5750\u5c31\u6ca1\u6709\u8c61\u9650\uff0c\u534a\u5f84\u4e0d\u53ef\u4ee5\u662f\u8d1f\u6570\u3002\u3002\u3002
r=2acos\u03b8\uff0c0<\u03b8<2/\u03c0
\u53ef\u4ee5\u5148\u7528\u76f4\u89d2\u5750\u6807\u5199\u51fa\u534a\u5706\u7684\u65b9\u7a0b\uff0c\u518d\u7528\u8f6c\u5316\u516c\u5f0f\u3002
绛旓細涓嶄竴鏍枫傜涓鍥撅紝鏋鍗婂緞r鐨鍙樺寲鑼冨洿鏄細浠巖=0鍙樺埌鐩寸嚎x=1鐨鏋佸潗鏍鏂圭▼r=1/cost涓殑1/cost锛屽嵆0銆妑銆1/cost銆傜浜屽浘锛宺浠庢洸绾縴=xx鍏ワ紝浠庢洸绾縳=1鍑猴紝鍦ㄦ瀬鍧愭爣涓嬶紝鍗筹紝浠巖sint=rrcostcost涓В鍑簉=sint/(cost)^2鍏ワ紝鑰屼粠rcost=1涓В鍑簉=1/cost鍑猴紝鍗硈int/(cost)^2銆妑銆1/cost銆
绛旓細鐩磋鍧愭爣杞崲鎴鏋佸潗鏍鍚 鍗婂緞r鐨涓婁笅闄愮‘瀹氭柟娉曪細鈶犵敾鍑虹Н鍒嗗尯鍩燂紝灏嗚竟鐣屾洸绾挎柟绋嬪寲鎴愭瀬鍧愭爣鏂圭▼銆傗憽浠庡潗鏍囧師鐐瑰嚭鍙戜綔灏勭嚎锛岀┛杩涘尯鍩熺偣鐨勬瀬寰勪负涓嬮檺锛岀┛鍑哄尯鍩熺偣鐨勬瀬寰勪负涓婇檺銆備緥濡傦細y=x^2 ===> r=sin胃/(cos胃)^2=sec胃tan胃锛泋=1 ===> r=sec胃銆備粠鍧愭爣鍘熺偣鍑哄彂浣滃皠绾匡紝浠庢姏鐗╃嚎...
绛旓細r鍦ㄤ笂闈㈢殑寮忓瓙閲屼笉鏄〃绀哄崐寰勶紝鑰屾槸璺濈銆r鏄瀬鍧愭爣涓婄殑鐐圭殑浣嶇疆鈥斺斾笌鍘熺偣璺濈涓簉锛屼笌x杞达紙姝ｆ柟鍚戯級澶硅涓何哥殑鐐广傚骞抽潰鐩磋鍧愭爣涓婄殑鐐圭殑浣嶇疆鐢紙x锛寉锛夎〃绀猴紝鏋佸潗鏍囦笂鐨勭偣鐨勪綅缃敤r鍜屛歌〃绀恒俽=2asin胃寮忎腑鐨勫浘褰紙鍦嗘垨鍦嗗姬锛鐨勫崐寰勬槸a銆
绛旓細甯︿笉甯︿笂涓嶆槸浣犺兘澶熼夋嫨鐨勩傛棦鐒舵槸杩樺師锛岄偅涔堣绉嚱鏁板氨鏄亽绛夊彉鎹紝鍙槸鑷彉閲忕殑褰㈠紡涓嶅悓鑰屽凡銆備綘涓嶅甫涓r鐨勮瘽锛岃绉嚱鏁颁笉灏卞彉浜嗗悧锛熼偅浣犵殑绛夊紡杩樿兘澶熸垚绔嬪悧锛
绛旓細涓嶅彲浠ャ傚洜灏忓渾鏂圭▼鏄 (x+1)^2+y^2=1, 鍗 x^2+y^2 = -2x 鍖涓烘瀬鍧愭爣鏄 r^2 = -2rcos胃, 鍗 r = -2cos胃 鏁 r 鐨勭Н鍒 鏄 0 鍒 -2cos胃锛岃 r 浠 0 绉埌 2 鏄湪澶у渾涓婄殑绉垎
绛旓細鏋佸潗鏍鍏紡鏄粈涔堬紵x = rcos(胃)锛寉 = rsin(胃)锛宺^2=x^2+y^2 锛堜竴鑸粯璁>0锛夛紝tan(胃)=y/x (x鈮0锛夈傚湪鏁板涓紝鏋佸潗鏍囩郴鏄竴涓簩缁村潗鏍囩郴缁熴傝鍧愭爣绯荤粺涓换鎰忎綅缃彲鐢变竴涓す瑙掑拰涓娈电浉瀵瑰師鐐光旀瀬鐐圭殑璺濈鏉ヨ〃绀恒傛瀬鍧愭爣绯荤殑搴旂敤棰嗗煙鍗佸垎骞挎硾锛屽寘鎷暟瀛︺佺墿鐞嗐佸伐绋嬨佽埅娴枫佽埅绌轰互鍙...
绛旓細鏋佸潗鏍 鏋佸潗鏍囩郴浠ｇ爜鏄16鐢ㄦ硶鍦54鍚庨潰鐩存帴鍔16浠ｈ〃鍗婂緞浠ｈ〃瑙掑害 濡傛灉浣犻棶鍦ㄥ潗鏍囩郴鏃嬭浆鐨勬槸浠涔堟剰鎬 閭ｅ氨鏄唬琛ㄧ殑鏄搴︿簡 浠ュ渾蹇冨悜x姝ｆ柟鍚戜负0搴 閫嗘椂閽堟棆杞 y姝ｆ柟鍚戞槸90 x璐熸柟鍚戞槸180 y璐熸柟鍚戞槸270
绛旓細鏍规嵁鍦嗗績鐨勪綅缃 褰撳渾蹇冧綅缃湪鍘熺偣鏃 r鐨勮寖鍥存槸鍙互鐢ㄦ暟瀛楄〃绀虹殑 褰撳渾蹇冪殑浣嶇疆涓嶅湪鍘熺偣鏃 闇瑕佺敤涓夎鍑芥暟琛ㄧずr
绛旓細r=cos胃鍦鏋佸潗鏍涓婄殑鍥惧儚鏄竴涓渾銆傝В锛氭湰棰樺埄鐢ㄤ簡鏋佸潗鏍囨潵鐢诲浘銆傚洜涓簆² = pcos胃 x² + y² = x (x - 1/2)² + y² = 1/4 鎵浠ョ敾鍑烘潵鏄釜鍦嗐
绛旓細胃 = arctan(y/x)锛涘湪x = 0鐨勬儏鍐典笅锛氳嫢y涓烘鏁拔 = 90掳锛涜嫢y涓鸿礋鏁锛屽垯胃 = 270掳 銆鏋佸潗鏍绯讳篃鏈変袱涓潗鏍囪酱锛歳锛鍗婂緞鍧愭爣锛夊拰胃锛堣鍧愭爣銆佹瀬瑙掓垨鏂逛綅瑙掞紝鏈夋椂涔熻〃绀轰负蠁鎴杢锛夈r鍧愭爣琛ㄧず涓庢瀬鐐圭殑璺濈锛屛稿潗鏍囪〃绀烘寜閫嗘椂閽堟柟鍚戝潗鏍囪窛绂0掳灏勭嚎锛堟湁鏃朵篃绉颁綔鏋佽酱锛夌殑瑙掑害銆
