若M={(x,y)||tanπy|+sin^2πx=0},N={(x,y)|x^2+y^2<=2},则M交N的元素个数是
tan\u03b1=m,\u03c0<\u03b1<2\u03c0,sin\u03b1=tan\u03b1=sin\u03b1/cos\u03b1=m
cos\u03b1=sin\u03b1/m
(sin\u03b1)^2+(cos\u03b1)^2=1
(sin\u03b1)^2+(sin\u03b1/m)^2=1
(m^2+1)/m^2*(sin\u03b1)^2=1
(sin\u03b1)^2=m^2/(m^2+1)
\u03c0<\u03b1<2\u03c0
sin\u03b1<0
sin\u03b1=-m/(m^2+1)^(1/2)
\u89e3:
M=sinatan(a/2)+cosa
=[2sin(a/2)cos(a/2)]*[sin(a/2)/cos(a/2)]+cosa
=[2sin^2(a/2)]+cosa
=2*[1-cosa]/2+cosa
=(1-cosa)+cosa
=1
\u6545\uff1aM=1
\u53c8\uff1atan(\u03c0/4)=2tan(\u03c0/8)/[1-tan^2(\u03c0/8)]
\u5219\uff1a
2tan(\u03c0/8)
=tan(\u03c0/4)[1-tan^2(\u03c0/8]
=1-tan^2(\u03c0/8)
\u5373\uff1atan^2(\u03c0/8)+2tan(\u03c0/8)=1
\u5219\uff1a
N=tan(\u03c0/8)[tan(\u03c0/8)+2]
=tan^2(\u03c0/8)+2tan(\u03c0/8)
=1
\u5219\uff1a
M=N=1
(B)
一个，{(0,0)}
绛旓細tan蟺y=0 sin2蟺x=0(杩欎釜搴旇娓呮) 鍙互寰楀埌 y=k x=0.5m (k,m涓轰换鎰忔暣鏁) 浠ｅ叆 x^2+y^2<=2 寰楀埌5k^2<=8锛堜负鏂逛究锛宬锛宮鐪嬪仛绛夋晥锛 鍥犳k,m鏈3涓 1锛-1 锛0 涓鍏9涓厓绱
绛旓細��绉泦X脳Y涓殑涓瀛愰泦R绉颁负X涓嶻鐨勪竴涓叧绯,鑻(x,y)鈭圧,鍒欑Оx涓巠鏈夊叧绯籖,璁颁负xRy.鑻(x,y)R,鍒欑Оx涓巠鏃犲叧绯. ��鐜拌f鏄疿涓嶻鐨勫叧绯,鍗砯X脳Y,濡傛灉(x,y),(x,z)鈭坒,蹇呮湁y=z,閭ｄ箞绉癴涓篨鍒癥鐨勫嚱鏁.鍦ㄦ瀹氫箟涓,宸插湪褰㈠紡涓婂洖閬夸簡鈥滃搴斺濈殑鏈,鍏ㄩ儴浣跨敤闆嗗悎璁虹殑璇█浜. ...
绛旓細[渚1]姹傚嚱鏁皔=cos2x-3sinx鐨勬渶澶у.瑙:y=cos2x-3sinx=-sin2x-3sinx+1=-(sinx+)2+ 鈭-1鈮inx鈮1,鈭村綋sinx=-1鏃,ymax=3 璇存槑:瑙ｆ棰樻槗蹇借sinx鈭圼-1,1]杩欎竴鑼冨洿,璁や负sinx=-鏃,y鏈夋渶澶у,閫犳垚璇В.浜,娉ㄦ剰鏉′欢涓鐨勮寖鍥 [渚2]宸茬煡|x|鈮,姹傚嚱鏁皔=cos2x+sinx鐨勬渶灏忓.瑙...
绛旓細璇佹槑濡備笅锛氳鍑芥暟f锛坸锛夊湪鏁伴泦A涓婃湁瀹氫箟锛屽鏋滃瓨鍦ㄥ父鏁M>0锛屼娇寰楀浠绘剰x锛鏈墊f(x)|<M 渚嬪锛屽嚱鏁 鍦ㄥ叾瀹氫箟鍩 鍐呮湁鐣岋紝杩欐槸鍥犱负瀵逛换鎰 鎬绘湁 鍐嶅锛屽嚱鏁 鍦ㄥ叾瀹氫箟鍩 鍐呮槸鏃犵晫鐨勶紝杩欐槸鍥犱负瀵逛换鎰忕殑瀹炴暟 鎬诲瓨鍦ㄧ偣 鏄剧劧 浣垮緱 鐒惰岋紝瀵逛换鎰忓疄鏁 鍑芥暟 鍦ㄥ畾涔夊煙鐨勫瓙闆 涓婂嵈鏄湁鐣岀殑锛岃繖鏄洜涓哄...
绛旓細y=|tanx|
绛旓細鍛ㄦ湡鎬э細鍛ㄦ湡涓簁蟺锛(k鈭坘Z)锛屾渶灏忔鍛ㄦ湡涓合 濂囧伓鎬э細鍋跺嚱鏁 鍗曡皟鎬э細鍦紙-蟺/2+k蟺锛0锛夊崟璋冮掑噺锛岋紙0锛屜/2+k蟺锛鍗曡皟閫掑 瀵圭О涓績锛氭棤 瀵圭О杞达細鐩寸嚎x=蟺/2+k蟺锛(k 鈭坺)姝ｅ鸡鍑芥暟 sin胃=y/r 浣欏鸡鍑芥暟 cos胃=x/r 姝ｅ垏鍑芥暟 tan胃=y/x 浣欏垏鍑芥暟 cot胃=x/y 姝ｅ壊鍑芥暟 sec胃=...
绛旓細4.璁緕=x+iy.鑻 (z)=my3+nx2y+i(x3-3xy2)涓鸿В鏋愬嚱鏁,鍒( )A.m=-3,n=-3 B.m=-3,n=1C.m=1,n=-3 D.m=1,n=15.绉垎 ( )A. B.1+iC. D. 6.璁綜鏄鍚戝渾鍛 鍒 =( )A. B. B. C. D. 7.璁綜鏄鍚戝渾鍛 ,鍒 =( )A. B. C. D.2 8.鐐箊=0鏄嚱鏁 鐨( )A.鍙幓...
绛旓細鍗 i=h / l, 鍧″害鐨勪竴鑸舰寮忓啓鎴 l : m 褰㈠紡锛屽i=1:5.濡傛灉鎶婂潯闈笌姘村钩闈㈢殑澶硅璁颁綔 a(鍙仛鍧¤锛夛紝閭ｄ箞 i=h/l=tan a.閿愯涓夎鍑芥暟鍏紡 姝ｅ鸡锛 sin 伪=鈭犖辩殑瀵硅竟/鈭犖 鐨勬枩杈 浣欏鸡锛歝os 伪=鈭犖辩殑閭昏竟/鈭犖辩殑鏂滆竟 姝ｅ垏锛歵an 伪=鈭犖辩殑瀵硅竟/鈭犖辩殑閭昏竟 浣欏垏锛歝ot 伪=鈭犖...
绛旓細sin^2锛堟淳x锛+|tan娲緔|=0 =>sin蟺x=0,tan蟺y=0 鈭聪x=2k蟺 , 蟺y=n蟺 (k,n鈭圸)=>x=2K, 鎴杫=n =>x=y=2m (m鈭圸)閫傚悎鏂圭▼sin^2锛堟淳x锛+|tan娲緔|=0鐨勭偣锛坸锛寉锛夌殑闆嗗悎{(x,y)lx=y=2m,m鈭圸}
