直线方程化为极坐标方程公式 怎么将直线的参数方程转化成极坐标方程？
\u76f4\u7ebf\u7684\u76f4\u89d2\u5750\u6807\u65b9\u7a0b\u600e\u4e48\u5316\u4e3a\u6781\u5750\u6807\u65b9\u7a0b\u6781\u5750\u6807\u7cfb\u4e0e\u5e73\u9762\u76f4\u89d2\u5750\u6807\u7cfb\u4e4b\u95f4\u7684\u53d8\u6362\uff1a
\u4ece\u6781\u5750\u6807 \u548c \u53ef\u4ee5\u53d8\u6362\u4e3a\u76f4\u89d2\u5750\u6807\uff1a
\u6216\uff1a
\u4ece\u76f4\u89d2\u5750\u6807 \u548c \u4e5f\u53ef\u4ee5\u53d8\u6362\u4e3a\u6781\u5750\u6807\uff1a
\u8fd9\u65b9\u7a0b\u5f0f\u7ed9\u51fa \u5728\u503c\u57df \u7684\u5f27\u5ea6\u3002\u6539\u7528\u89d2\u5ea6\u5355\u4f4d\uff0c\u503c\u57df\u4e3a \u3002
\u8fd9\u4e9b\u65b9\u7a0b\u5f0f\u5047\u5b9a\u6781\u70b9\u662f\u76f4\u89d2\u5750\u6807\u7cfb\u7684\u539f\u70b9 \uff0c\u6781\u8f74\u4e3ax-\u5750\u6807\u8f74\uff0c\u800cy-\u5750\u6807\u8f74\u65b9\u5411\u7684\u5f27\u5ea6\u4e3a \uff0c\u89d2\u5ea6\u4e3a +90\u5ea6\u3002
\u62d3\u5c55\u8d44\u6599\uff1a
\u5728\u6570\u5b66\u4e2d\uff0c\u6781\u5750\u6807\u7cfb\u662f\u4e00\u4e2a\u4e8c\u7ef4\u5750\u6807\u7cfb\u7edf\u3002\u8be5\u5750\u6807\u7cfb\u7edf\u4e2d\u4efb\u610f\u4f4d\u7f6e\u53ef\u7531\u4e00\u4e2a\u5939\u89d2\u548c\u4e00\u6bb5\u76f8\u5bf9\u539f\u70b9\u2014\u6781\u70b9\u7684\u8ddd\u79bb\u6765\u8868\u793a\u3002\u6781\u5750\u6807\u7cfb\u7684\u5e94\u7528\u9886\u57df\u5341\u5206\u5e7f\u6cdb\uff0c\u5305\u62ec\u6570\u5b66\u3001\u7269\u7406\u3001\u5de5\u7a0b\u3001\u822a\u6d77\u3001\u822a\u7a7a\u4ee5\u53ca\u673a\u5668\u4eba\u9886\u57df\u3002
\u5728\u4e24\u70b9\u95f4\u7684\u5173\u7cfb\u7528\u5939\u89d2\u548c\u8ddd\u79bb\u5f88\u5bb9\u6613\u8868\u793a\u65f6\uff0c\u6781\u5750\u6807\u7cfb\u4fbf\u663e\u5f97\u5c24\u4e3a\u6709\u7528\uff1b\u800c\u5728\u5e73\u9762\u76f4\u89d2\u5750\u6807\u7cfb\u4e2d\uff0c\u8fd9\u6837\u7684\u5173\u7cfb\u5c31\u53ea\u80fd\u4f7f\u7528\u4e09\u89d2\u51fd\u6570\u6765\u8868\u793a\u3002
\u5bf9\u4e8e\u5f88\u591a\u7c7b\u578b\u7684\u66f2\u7ebf\uff0c\u6781\u5750\u6807\u65b9\u7a0b\u662f\u6700\u7b80\u5355\u7684\u8868\u8fbe\u5f62\u5f0f\uff0c\u751a\u81f3\u5bf9\u4e8e\u67d0\u4e9b\u66f2\u7ebf\u6765\u8bf4\uff0c\u53ea\u6709\u6781\u5750\u6807\u65b9\u7a0b\u80fd\u591f\u8868\u793a\u3002
绛旓細鐩寸嚎鏂圭▼鍖栦负鏋佸潗鏍囨柟绋嬪叕寮弜=蟻cos胃锛寉=蟻sin胃銆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婃満鍣ㄤ汉棰嗗煙銆傚浜庡緢澶氱被鍨嬬殑鏇茬嚎锛屾瀬鍧愭爣鏂圭▼鏄渶绠鍗曠殑琛ㄨ揪褰㈠紡锛岀敋鑷...
绛旓細鐩寸嚎鐨勬瀬鍧愭爣鏂圭▼鏄細瀵逛簬涓嶇粡杩囨瀬鐐圭殑鐩寸嚎y锛漦x锛媌,浠ｅ叆x锛澫乧os胃,y锛澫乻in胃,鍖栫畝鍗冲彲銆備竴銆佹蹇 鏋佸潗鏍囩郴锛坧olar coordinates锛夋槸鎸囧湪骞抽潰鍐呯敱鏋佺偣銆佹瀬杞村拰鏋佸緞缁勬垚鐨勫潗鏍囩郴銆傚湪骞抽潰涓婂彇瀹氫竴鐐筄锛岀О涓烘瀬鐐广備粠O鍑哄彂寮曚竴鏉″皠绾縊x锛岀О涓烘瀬杞淬傚啀鍙栧畾涓涓崟浣嶉暱搴︼紝閫氬父瑙勫畾瑙掑害鍙栭嗘椂閽堟柟鍚戜负姝...
绛旓細鐩寸嚎鐨勬瀬鍧愭爣鏂圭▼鍏紡涓合=x²+y²锛宼an胃=y/x 锛屾渶鍚庤浆鎹负蟻*cos(胃-a)=d 锛涜屼笖鍏朵腑蟻鍜屛告槸鍙橀噺锛宎鍜宒鏄緟瀹氶噺锛岄氳繃缁欏嚭鐨勪袱涓畾鐐圭殑鍧愭爣鍊兼潵纭畾銆傜洿绾跨敱鏃犳暟涓偣鏋勬垚锛屾槸闈㈢殑缁勬垚鎴愬垎锛屽苟缁ц岀粍鎴愪綋锛涜屼笖鐩寸嚎娌℃湁绔偣锛屽悜涓ょ鏃犻檺寤堕暱锛岄暱搴︽棤娉曞害閲忥紱骞朵笖鐩寸嚎涔熸槸杞村绉...
绛旓細鈭 鏋佸潗鏍囨柟绋嬩负 r=sec胃*tan胃
绛旓細璁鐩寸嚎鏂圭▼涓篺(x,y)=0鍒╃敤鐐(x,y)瀵瑰簲(蟻,胃)鐨杞崲鍏紡蟻=x²+y²,tan胃=y/x鍙皢f(x,y)=0杞崲涓g(蟻,胃)=0 杩介棶 鍙互涓句釜渚嬪瓙鍚 杩界瓟 姣斿宸茬煡鐩寸嚎2x+y锕3=0鍒2(蟻cos胃)+(蟻sin胃)锕3=0鍗诚(2cos胃+sin胃)=3濡傛灉浣犳効鎰,鍙互鍒╃敤杈呭姪瑙掑叕寮忓皢2cos胃+sin胃鍖栦负鈭5sin(胃+...
绛旓細鐩寸嚎鐨鏋佸潗鏍囨柟绋鏄痑蟻cos胃+b蟻sin胃+c=0銆傝鐩寸嚎鏂圭▼涓 ax+by+c=0锛屽湪鏋佸潗鏍囩郴涓瓁=rsin胃锛寉=rcos胃锛屼唬鍏ュ彲寰梐蟻cos胃+b蟻sin胃+c=0銆
绛旓細鍋囪鐩寸嚎ax+by+c=0 鍒╃敤x=pcos胃锛寉=psin胃 鍖栦负鏋佸潗鏍涓篴pcos胃+bpsin胃+c=0.鏋佸潗鏍囩郴鎻忚堪鐨勬洸绾挎柟绋嬬О浣鏋佸潗鏍囨柟绋锛岄氬父琛ㄧず涓簉涓鸿嚜鍙橀噺胃鐨勫嚱鏁般傛瀬鍧愭爣鏂圭▼缁忓父浼氳〃鐜板嚭涓嶅悓鐨勫绉板舰寮忥紝濡傛灉r(−胃) = r(胃)锛屽垯鏇茬嚎鍏充簬鏋佺偣(0掳/180掳)瀵圭О锛屽鏋渞(蟺+胃) = r(胃)锛屽垯...
绛旓細鍦ㄦ瀬鍧愭爣绯讳腑锛鐩寸嚎鍙互鐢鏋佸潗鏍囨柟绋 r = a/ cos(胃-伪) 琛ㄧず锛屽叾涓 a 鏄洿绾垮埌鍘熺偣鐨勬湁鍚戣窛绂伙紝伪 鏄洿绾夸笌 x 杞翠箣闂寸殑澶硅銆傝璁＄畻涓鏉＄洿绾跨殑鏋佸潗鏍囨柟绋嬶紝鍙互鎸夌収浠ヤ笅姝ラ杩涜锛氬皢鐩寸嚎鐨勪竴鑸鏂圭▼杞崲涓鏂滄埅寮忔柟绋 y = mx + b 鎴栬呮埅璺濆紡鏂圭▼ x/a + y/b = 1锛屽叾涓 m 鏄枩鐜囷紝a ...
绛旓細鐩寸嚎鐨鏋佸潗鏍囨柟绋鏄細A蟻cos胃+b蟻sin胃+c=0銆傚湪骞抽潰鍐呭彇涓涓畾鐐筄锛屽彨鏋佺偣锛屽紩涓鏉″皠绾縊x锛屽彨鍋氭瀬杞达紝鍐嶉夊畾涓涓暱搴﹀崟浣嶅拰瑙掑害鐨勬鏂瑰悜锛堥氬父鍙栭嗘椂閽堟柟鍚戯級銆傚浜庡钩闈㈠唴浠讳綍涓鐐筂锛岀敤蟻琛ㄧず绾挎OM鐨勯暱搴︼紝胃琛ㄧず浠嶰x鍒癘M鐨勮搴︼紝蟻鍙仛鐐筂鐨勬瀬寰勶紝胃鍙仛鐐筂鐨勬瀬瑙掞紝鏈夊簭鏁板 (蟻,胃)灏卞彨...
绛旓細鎶婄洿瑙掑潗鏍囩郴涓紙x,y锛夛紝x鐢ㄏ乧os胃浠ｆ浛锛寉鐢ㄏ乻in胃浠ｆ浛锛岀洿鎺ュ甫鍏ュ嵆鍙傝鏇茬嚎C鐨鏋佸潗鏍囨柟绋嬩负r=r锛埼革級锛屽垯C鐨勫弬鏁版柟绋嬩负x=r锛埼革級cos胃锛寉=r锛埼革級sin胃锛屽叾涓镐负鏋佽銆傜敱鍙傛暟鏂圭▼姹傚娉曪紝寰楁洸绾緾鐨勫垏绾垮x杞寸殑鏂滅巼涓簓藠=r藠(胃)sin胃+r(胃)cos胃鈭時藠(胃)cos胃-r(胃)sin胃...
