正余弦函数的性质(最值与单调性) 正余弦函数的单调性和最值，6和9，9要过程
\u9ad8\u4e00\u6570\u5b66\u9898\uff1a\u6b63\u5f26\u51fd\u6570\uff0c\u4f59\u5f26\u51fd\u6570\u7684\u6027\u8d28\u2014 \u5947\u5076\u6027\uff0c\u5355\u8c03\u6027\uff0c\u6700\u503c\uff081\uff09\u51fd\u6570f(x)\u7684\u5355\u8c03\u9012\u51cf\u533a\u95f4\uff1apai/2+2kpai<=x-pai/4<=3/2pai+2kpai
\u533a\u95f4\u4e3a[\uff083/4\uff09pai+2kpai,\uff087/4\uff09pai+2kpai]k\u4e3a\u6574\u6570
\uff082\uff09f(x)\u5728[0,pai],\u6700\u503c\u57280,3/4\u03c0\u4e0a\u53d6\u5f97\uff0c
f(0)=b,f(3/4\u03c0)=b+(\u6839\u53f72+1)a
a<0,b=3,a=1-\u6839\u53f72
y=\u221a\uff081-1/2cosx)
\u56e0\u4e3acosx\u5f97\u503c\u57df\u662f-1\u52301\uff08\u5305\u542b-1\u4e0e1\uff09
\u6240\u4ee51-1/2cosx\u7684\u503c\u57df\u5c31\u662f1/2\u52303/2
绛旓細1.4.2姝ｅ鸡銆浣欏鸡鍑芥暟鐨勬ц川姝ｅ鸡銆佹寮︽渶鍊间笌鍗曡皟鎬э級锛堟渶鍊间笌鍗曡皟鎬锛夎鍚屽鐢熶滑鍥炲繂涓姝ｄ綑寮﹀嚱鏁扮殑鏈鍊紋1−35蟺蟺−2−2蟺−3蟺2−蟺−蟺2O蟺2蟺−13蟺22蟺5蟺23蟺x鏈澶у硷細鏈澶у硷細褰搙=蟺2+2k蟺(k鈭圸)鏈夋渶澶у紋=1+2k蟺(k鈭圸)鏈夋渶...
绛旓細2銆佷綑寮﹀嚱鏁帮細锛1锛夊浘鍍忥細锛2锛夋ц川锛鈶犲懆鏈熸э細鏈灏忔鍛ㄦ湡閮芥槸2蟺 鈶″鍋舵э細鍋跺嚱鏁 鈶㈠绉版э細瀵圭О涓績鏄(K蟺+蟺/2,0)锛孠鈭圸锛涘绉拌酱鏄洿绾縳=K蟺锛孠鈭圸 鈶ｅ崟璋冩э細鍦╗2K蟺,2K蟺+蟺]锛孠鈭圸涓婂崟璋冮掑噺锛涘湪[2K蟺+蟺,2K蟺+2蟺]锛孠鈭圸涓婂崟璋冮掑 锛3锛夊畾涔夊煙锛歊 锛4锛夊煎煙锛歔-...
绛旓細浣欏鸡鍑芥暟鐨瀹氫箟鍩熸槸鏁翠釜瀹炴暟闆嗭紝鍊煎煙鏄痆-1,1]銆傚畠鏄懆鏈熷嚱鏁帮紝鍏舵渶灏忔鍛ㄦ湡涓2蟺銆
绛旓細褰撳嚱鏁 f(x) 鐨勮嚜鍙橀噺鍦ㄥ叾瀹氫箟鍖洪棿鍐呭澶э紙鎴栧噺灏忥級鏃讹紝鍑芥暟鍊糵(x)涔熼殢鐫澧炲ぇ锛堟垨鍑忓皬锛锛屽垯绉拌鍑芥暟涓哄湪璇ュ尯闂翠笂鍏锋湁鍗曡皟鎬с傚鏋滆鏄庝竴涓嚱鏁板湪鏌愪釜鍖洪棿D涓婂叿鏈夊崟璋冩э紝鍒欐垜浠皢D绉颁綔鍑芥暟鐨勪竴涓崟璋冨尯闂达紝鍒欏彲鍒ゆ柇鍑猴細1銆丏⊆Q锛圦鏄嚱鏁扮殑瀹氫箟鍩燂級銆2銆佸尯闂碊涓婏紝瀵逛簬鍑芥暟f(x)锛W...
绛旓細1. 姝ｅ鸡鍑芥暟锛坰in(x)锛夌殑鍗曡皟鎬э細- 鍦ㄥ尯闂 [0, 蟺] 涓婏紝姝ｅ鸡鍑芥暟鏄掑鐨勶紝鍗 sin(x) 鍦ㄨ鍖洪棿鍐呭崟璋冮掑銆- 鍦ㄥ尯闂 [蟺, 2蟺] 涓婏紝姝ｅ鸡鍑芥暟鏄掑噺鐨勶紝鍗 sin(x) 鍦ㄨ鍖洪棿鍐呭崟璋冮掑噺銆2. 浣欏鸡鍑芥暟锛坈os(x)锛夌殑鍗曡皟鎬э細- 鍦ㄥ尯闂 [0, 蟺/2] 涓婏紝浣欏鸡鍑芥暟鏄掑噺鐨勶紝鍗 cos(x) ...
绛旓細鏈灏忓间负Y=b-A 锛屾眰鍑芥暟鐨鍛ㄦ湡鍙互鍒╃敤T=2蟺/w锛堟鍒囧嚱鏁版槸T=蟺/w)浣欏鸡鍑芥暟cosx鏄皢姝ｅ鸡鍑芥暟sinx鍚戝乏骞崇Щ蟺/2鍗曚綅寰楀埌鐨勶紝鏄撳緱瀹冩槸鍋跺嚱鏁帮紝鍊煎煙涓巗inx鐩稿悓锛鎬ц川鍙互鍙傜収涓婅堪姝ｅ鸡鍑芥暟鎺ㄥ緱銆傚叾瀹炶繖浜涘湪涔︿笂灏辨湁锛岃繕鏈変笂璇捐佸笀鍒拌繖涓湴鏂逛竴鑸兘鏈夎缁嗚鐨勩備綘浠旂粏鐪嬩竴涓嬬瑪璁帮紝濡傛灉杩樻槸涓嶆噦锛...
绛旓細姝ｅ鸡浣欏鸡鍑芥暟鐨鍛ㄦ湡閮芥槸2蟺銆傛荤粨 1銆佸畾涔夊煙锛歽=sinx瀹氫箟鍩熶负R銆2銆佸煎煙锛氬紩瀵煎鐢熷洖蹇嗗崟浣嶅渾涓殑姝ｅ鸡鍑芥暟绾匡紝鍙戠幇鍊煎煙涓篬-1,1]銆3銆鏈鍊锛氭牴鎹煎煙鐨勭‘瀹氬緱鍒板湪浣曞鍙栧緱鏈鍊间互鍙婂嚱鏁扮殑姝ｈ礋鎬с6銆鍗曡皟鎬锛氭渶鍚庤瀛︾敓鏍规嵁鍒氭墠鎵寰楀埌鐨勭粨璁鸿嚜宸卞皾璇曟荤粨姝ｅ鸡鍑芥暟鐨勫崟璋冩с傚湪鎺㈢┒瀹屾寮鍑芥暟鎬ц川鍚庯紝...
绛旓細姝ｅ鸡锛浣欏鸡鍑芥暟鐨瀹氫箟鍩熶负R锛屽煎煙涓篬-1,1]姝ｅ鸡:鍗曡皟澧炲尯闂翠负[-pi/2+2kpi,pi/2+2kpi]鍗曡皟鍑忓尯闂翠负[pi/2+2kpi,3pi/2+2kpi]浣欏鸡:鍗曡皟澧炲尯闂翠负[-pi+2kpi,2kpi]鍗曡皟鍑忓尯闂翠负[2kpi,pi+2kpi]pi鏄偅涓鍙峰渾鍛ㄧ巼
绛旓細姝ｅ鸡锛浣欏鸡鍑芥暟鐨瀹氫箟鍩熶负r锛屽煎煙涓篬-1,1]姝ｅ鸡:鍗曡皟澧炲尯闂翠负[-pi/2+2kpi,pi/2+2kpi]鍗曡皟鍑忓尯闂翠负[pi/2+2kpi,3pi/2+2kpi]浣欏鸡:鍗曡皟澧炲尯闂翠负[-pi+2kpi,2kpi]鍗曡皟鍑忓尯闂翠负[2kpi,pi+2kpi]pi鏄偅涓鍙峰渾鍛ㄧ巼
绛旓細鈶犳渶澶у硷細褰搙=2k蟺+(蟺/2) 锛宬鈭圸鏃讹紝y(max)=1 鈶℃渶灏忓硷細褰搙=2k蟺+(3蟺/2)锛宬鈭圸鏃讹紝y(min)=-1 闆跺肩偣锛 (k蟺,0) 锛宬鈭圸 姝ｅ垏鍑芥暟y=tanx鍦ㄥ紑鍖洪棿锛坸鈭(-蟺/2,蟺/2)锛夌殑鍙嶅嚱鏁帮紝璁颁綔y=arctanx 鎴 y=tan-1x锛屽彨鍋氬弽姝ｅ垏鍑芥暟銆傚弽姝ｅ垏鍑芥暟鐨瀹氫箟鍩熶负R鍗(-鈭烇紝+鈭...
