极坐标系中直线ρsinθ＝-2怎样化为普通直角坐标方程 在极坐标系中，直线l的极坐标方程为ρsin（θ+π8）=2，...
\u5c06\u66f2\u7ebf\u6781\u5750\u6807\u65b9\u7a0b\u03c1=-2sin\u03b8\u5316\u4e3a\u76f4\u89d2\u5750\u6807\u65b9\u7a0b\u03c1=-2sin\u03b8
\u03c1²=-2\u03c1sin\u03b8
\u03c1²=x²+y²\uff0c\u03c1sin\u03b8=y\u4ee3\u5165\uff0c\u5f97x²+y²=-2y
x²+y²+2y=0
x²+y²+2y+1=1
x²+(y+1)²=1
\u6240\u6c42\u76f4\u89d2\u5750\u6807\u65b9\u7a0b\u4e3ax²+(y+1)²=1\uff0c\u662f\u4ee5(0\uff0c-1)\u4e3a\u5706\u5fc3\uff0c1\u4e3a\u534a\u5f84\u7684\u5706\u3002
\u2235cos\u03c08=1+cos\u03c042=2+22 sin\u03c08=1?cos\u03c042=2?22\uff0c\u518d\u6839\u636ex=\u03c1cos\u03b8\uff0cy=\u03c1sin\u03b8\uff0c\u628a\u76f4\u7ebfl\u7684\u6781\u5750\u6807\u65b9\u7a0b\u4e3a\u03c1sin\uff08\u03b8+\u03c08\uff09=2\u5316\u4e3a\u76f4\u89d2\u5750\u6807\u65b9\u7a0b\u4e3a<div style="width:6px;background: url('http://hiph
有公式y=ρsinθ极坐标系中直线ρsinθ＝-2
就是普通直角坐标方程y=-2
绛旓細鐩寸嚎鐨鏋佸潗鏍鏂圭▼鏄 鍏朵腑锛岀粡杩囨瀬鐐圭殑灏勭嚎鐨勬瀬鍧愭爣鏂圭▼鐢卞涓嬫柟绋嬭〃绀猴細胃=蠁锛屽叾涓嗕负灏勭嚎鐨勫炬枩瑙掑害锛岃嫢 k涓虹洿瑙鍧愭爣绯鐨勫皠绾跨殑鏂滅巼锛屽垯鏈壪 = arctan k銆 浠讳綍涓嶇粡杩囨瀬鐐圭殑鐩寸嚎閮戒細涓庢煇鏉″皠绾垮瀭鐩淬 杩欎簺鍦ㄧ偣锛 锛屜嗭級澶勭殑鐩寸嚎涓庡皠绾胃 = 蠁 鍨傜洿銆
绛旓細4蟻²=蟻sin胃+蟻cos胃浠=蟻cos胃銆亂=蟻sin胃,鍒櫹²=x²+y²,浠ｅ叆涓婂紡寰楀渾c鐨勭洿瑙鍧愭爣鏂圭▼涓:鍦哻:4(x²+y²)=x+y,鍗(x+1/8)²+(y+1/8)²=1/32鎵浠ュ渾蹇僣涓(-1/8,-1/8),鍗婂緞r=鈭2/8杩愮敤鐐瑰埌鐩寸嚎鐨勮窛绂,鍙眰寰楀渾蹇僣鍒扮洿绾縧鐨勮窛绂讳负d=|2*(-1/8)-...
绛旓細灏嗗師鏋佸潗鏍鏂圭▼涓簆=2sin胃锛屽寲鎴愶細p 2 =2蟻sin胃锛屽叾鐩磋鍧愭爣鏂圭▼涓猴細鈭磝 2 +y 2 =2y锛屾槸涓涓崐寰勪负1鐨勫渾锛屽叾闈㈢Н涓合锛庢晠绛旀涓猴細蟺锛
绛旓細鍦蟻=2cos胃 鍗 蟻 2 =2蟻cos胃锛屽嵆 x 2 +y 2 =2x锛屽嵆 锛坸-1锛 2 +y 2 =1锛岃〃绀轰互锛1锛0锛変负鍦嗗績锛屽崐寰勭瓑浜1鐨勫渾锛庡渾蹇冨埌鐩寸嚎鐨勮窛绂讳负 |1-0+1| 2 = 2 锛1=r锛屾晠鐩寸嚎鍜屽渾鐩哥锛屾晠绛旀涓 鐩哥锛
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ｃ傝繖鏍凤紝...
绛旓細鏋佸潗鏍囬潰绉厓鐨勫叕寮忔庝箞寰楁潵鐨 d胃鏄瀬鍧愭爣鐨勬瀬瑙捨哥殑澧為噺.闈㈢Нs杩戜技绛変簬鎵囧舰鐨勯潰绉=1/2*r^2d胃(杩欓噷锛歳鏄瀬缁,d胃鏄渾蹇冭锛夈傚渾鐨勬瀬鍧愭爣鍏紡锛毾=x+y锛寈=蟻cos胃锛寉=蟻sin胃锛宼an胃=y/x锛岋紙x涓嶄负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燂紝璇ュ潗鏍囩郴缁熶腑浠绘剰浣嶇疆鍙湁涓涓す瑙掑拰涓...
绛旓細蟻= 1 cos胃-2sin胃 锛屽緱鍏剁洿瑙掑潗鏍囨柟绋嬩负锛歺-2y=1鍏充簬x杞村绉板悗鐨勬洸绾挎柟绋嬩负x+2y=1鈭村叧浜庢瀬杞寸殑瀵圭О鏇茬嚎鐨鏋佸潗鏍鏂圭▼涓 蟻= 1 cos胃+2sin胃 鏁呴堿锛
绛旓細鍦鏋佸潗鏍囩郴涓锛岀洿绾 蟻cos胃=2 涓鐩寸嚎 蟻sin胃=2 鍏充簬鐩寸嚎 胃=蟺/4 瀵圭О銆傜浉褰撲簬 鐩磋鍧愭爣绯讳腑鐨勭洿绾 x=2 涓庣洿绾 y=2 鍏充簬鐩寸嚎 y=x 瀵圭О銆傚洜姝 蟻sin胃=2 涓 y=2 閮芥槸姝ｇ‘鐨勩傜敱浜庨鐩腑鍑虹幇鐨勯兘鏄瀬鍧愭爣鏂圭▼锛屽彲鑳藉～ 蟻sin胃=2 濂戒竴浜 ...
绛旓細鏂圭▼鍖栦负 蟻sin胃cos(蟺/6)+蟻cos胃sin(蟺/6) = 2 ,鎵浠 鈭3/2*蟻sin胃+1/2*蟻cos胃 = 2 ,鍖栦负鐩磋鍧愭爣灏辨槸 鈭3/2*y+1/2*x = 2 ,鎵浠,鐩寸嚎鐨勬枩鐜囦负 k = -(1/2) / (鈭3/2) = -鈭3/3 ,鍥犳,鐩寸嚎鍊炬枩瑙掍负 arctan(-鈭3/3) = 5蟺/6 .
绛旓細鍒╃敤鍏紡锛歺=蟻cos胃锛寉=蟻sin胃锛岀洿鎺ュ皢x鍜寉浣滀唬鎹㈠悗浠ｅ叆鍘熸柟绋嬶紝鍗冲彲灏嗙洿瑙掑潗鏍囨柟绋嬪寲涓鏋佸潗鏍鏂圭▼銆備緥锛歽=x²x=蟻cos胃锛寉=蟻sin胃浠ｅ叆涓婂紡寰楋細蟻sin胃=(蟻cos胃)²sin胃=蟻cos²胃 鍗充负鏋佸潗鏍囨柟绋嬨
