函数y=cos^2(x)-sinx的值域是？ 函数y=cos（sinx）的值域是？？？
\u51fd\u6570y=cos^2x-sinx\u7684\u503c\u57df\u662fy=cos^2x-sinx=1-\uff08sinx\uff09^2-sinx=5/4-(sinx+1/2)^2\uff1b
sinx\u2208[-1,1],(sinx+1/2)^2\u2208[0,9/4]\uff1b
\u6240\u4ee5\u503c\u57dfy\u2208[-1,5/4]
\u503c\u57df\uff1a\u56e0\u53d8\u91cf\u6539\u53d8\u800c\u6539\u53d8\u7684\u53d6\u503c\u8303\u56f4\u53eb\u505a\u8fd9\u4e2a\u51fd\u6570\u7684\u503c\u57df\uff0c\u5728\u51fd\u6570\u73b0\u4ee3\u5b9a\u4e49\u4e2d\u662f\u6307\u5b9a\u4e49\u57df\u4e2d\u6240\u6709\u5143\u7d20\u5728\u67d0\u4e2a\u5bf9\u5e94\u6cd5\u5219\u4e0b\u5bf9\u5e94\u7684\u6240\u6709\u7684\u8c61\u6240\u7ec4\u6210\u7684\u96c6\u5408\u3002
\u4e09\u89d2\u51fd\u6570\u662f\u6570\u5b66\u4e2d\u5e38\u89c1\u7684\u4e00\u7c7b\u5173\u4e8e\u89d2\u5ea6\u7684\u51fd\u6570\u3002\u4e5f\u53ef\u4ee5\u8bf4\u4ee5\u89d2\u5ea6\u4e3a\u81ea\u53d8\u91cf\uff0c\u89d2\u5ea6\u5bf9\u5e94\u4efb\u610f\u4e24\u8fb9\u7684\u6bd4\u503c\u4e3a\u56e0\u53d8\u91cf\u7684\u51fd\u6570\u53eb\u4e09\u89d2\u51fd\u6570\uff0c\u4e09\u89d2\u51fd\u6570\u5c06\u76f4\u89d2\u4e09\u89d2\u5f62\u7684\u5185\u89d2\u548c\u5b83\u7684\u4e24\u4e2a\u8fb9\u957f\u5ea6\u7684\u6bd4\u503c\u76f8\u5173\u8054\uff0c\u4e5f\u53ef\u4ee5\u7b49\u4ef7\u5730\u7528\u4e0e\u5355\u4f4d\u5706\u6709\u5173\u7684\u5404\u79cd\u7ebf\u6bb5\u7684\u957f\u5ea6\u6765\u5b9a\u4e49\u3002\u4e09\u89d2\u51fd\u6570\u5728\u7814\u7a76\u4e09\u89d2\u5f62\u548c\u5706\u7b49\u51e0\u4f55\u5f62\u72b6\u7684\u6027\u8d28\u65f6\u6709\u91cd\u8981\u4f5c\u7528\uff0c\u4e5f\u662f\u7814\u7a76\u5468\u671f\u6027\u73b0\u8c61\u7684\u57fa\u7840\u6570\u5b66\u5de5\u5177\u3002\u5728\u6570\u5b66\u5206\u6790\u4e2d\uff0c\u4e09\u89d2\u51fd\u6570\u4e5f\u88ab\u5b9a\u4e49\u4e3a\u65e0\u7a77\u7ea7\u9650\u6216\u7279\u5b9a\u5fae\u5206\u65b9\u7a0b\u7684\u89e3\uff0c\u5141\u8bb8\u5b83\u4eec\u7684\u53d6\u503c\u6269\u5c55\u5230\u4efb\u610f\u5b9e\u6570\u503c\uff0c\u751a\u81f3\u662f\u590d\u6570\u503c\u3002
\u5e38\u89c1\u7684\u4e09\u89d2\u51fd\u6570\u5305\u62ec\u6b63\u5f26\u51fd\u6570\u3001\u4f59\u5f26\u51fd\u6570\u548c\u6b63\u5207\u51fd\u6570\u3002\u5728\u822a\u6d77\u5b66\u3001\u6d4b\u7ed8\u5b66\u3001\u5de5\u7a0b\u5b66\u7b49\u5176\u4ed6\u5b66\u79d1\u4e2d\uff0c\u8fd8\u4f1a\u7528\u5230\u5982\u4f59\u5207\u51fd\u6570\u3001\u6b63\u5272\u51fd\u6570\u3001\u4f59\u5272\u51fd\u6570\u3001\u6b63\u77e2\u51fd\u6570\u3001\u4f59\u77e2\u51fd\u6570\u3001\u534a\u6b63\u77e2\u51fd\u6570\u3001\u534a\u4f59\u77e2\u51fd\u6570\u7b49\u5176\u4ed6\u7684\u4e09\u89d2\u51fd\u6570\u3002\u4e0d\u540c\u7684\u4e09\u89d2\u51fd\u6570\u4e4b\u95f4\u7684\u5173\u7cfb\u53ef\u4ee5\u901a\u8fc7\u51e0\u4f55\u76f4\u89c2\u6216\u8005\u8ba1\u7b97\u5f97\u51fa\uff0c\u79f0\u4e3a\u4e09\u89d2\u6052\u7b49\u5f0f\u3002
\u4ee4t=sinx,\u5219
-1=<t<=1
cos1=<cost<=1
\u6240\u4ee5y\u7684\u503c\u57df\u4e3a[cos1, 1]
\u5982\u679c\u6709\u5e2e\u5230\u60a8 \u8bf7\u7ed9\u4e88\u597d\u8bc4 \u8c22\u8c22\u62c9#^_^#\u795d\u60a8\u6109\u5feb
=-sin²(x)-sinx+1
=5/4-(sinx+1/2)²
∵-1≤sinx≤1
∴-1/2≤sinx+1/2≤3/2
∴ 0≤(sinx+1/2)²≤9/4
-1≤y≤5/4
y值域(-1, 5/4)
y=cos²x-sinx
=(cos²x-1+1)-sinx
= -sin²x-sinx+1
=5/4-(sinx+1/2)²
因为-1≤sinx≤1
所以-1/2≤sinx+1/2≤3/2
所以0≤(sinx+1/2)²≤9/4
所以-1≤5/4-(sinx+1/2)²≤5/4
所以值域为[-1,5/4]
y=cos^2(x)-sinx
=1-sin^2(x)-sinx
=-(sinx+1/2)^2+5/4
-1<=sinx<=1
-1/2<=(sinx+1/2)<=3/2
0<=(sinx+1/2)^2<=9/4
-9/4<=-(sinx+1/2)^2<=0
-1<=-(sinx+1/2)^2+5/4<=5/4
-1<=y<=5/4
1、y=cos^2(x)-sinx=1-sin^2(x)-sinx=-(sin^2(x)+sinx-1)=-(sinx+1/2)^2+5/4
2、sinx+1/2的值域是（-1/2,3/2),
3、(sinx+1/2)^2的值域是（1/4,9/4)，-(sinx+1/2)^2的值域是（-9/4,0)
4、-(sinx+1/2)^2+5/4的值域是（-1,5/4)
5、注以上均为闭区间
y=cos(x)*cos(x)-sin(x)
=1-sin(x)^2-sin(x)
=1-(sin(x)^2+sin(x))
=1-(sin(x)^2+sin(x)+(1/2)^2-(1/2)^2)
=1-(sin(x)+1/2)^2+1/4
=5/4-(sin(x)+1/2)^2
sin(x)=-1/2时，是y最大值5/4
sin(x)=1是，是y的最小值-1
我提供哈思路吧把COS(X)2用1-SIN（X)2代替 然后再配方即可
绛旓細姝ｅ鸡鍑芥暟锛歴in胃锛漼/r 浣欏鸡鍑芥暟锛歝os胃锛漻/r 姝ｅ垏鍑芥暟锛歵an胃锛漼/x 浣欏垏鍑芥暟锛歝ot胃锛漻/y 姝ｅ壊鍑芥暟锛歴ec胃锛漴/x 浣欏壊鍑芥暟锛歝sc胃锛漴/y 鍚岃涓夎鍑芥暟闂寸殑鍩烘湰鍏崇郴寮忥細骞虫柟鍏崇郴锛歴in^2(伪锛+cos^2(伪锛=1 tan^2(伪锛+1=sec^2(伪锛塩ot^2(伪锛+1=csc^2(伪锛夌Н鐨勫叧绯伙細sin伪锛漷an...
绛旓細姝ｅ壊鐨勮嫳鏂囨槸Secant锛岃闊虫槸['siːkənt]锛涗綑鍓茬殑鑻辨枃鏄疌osecant锛岃闊虫槸['kəʊ'siːkənt]銆傛鍓诧紙Secant锛宻ec锛夋槸涓夎鍑芥暟鐨勪竴绉嶃傚畠鐨勫畾涔夊煙涓嶆槸鏁翠釜瀹炴暟闆嗭紝鍊煎煙鏄粷瀵瑰煎ぇ浜庣瓑浜庝竴鐨勫疄鏁般傚畠鏄懆鏈熷嚱鏁帮紝鍏舵渶灏忔鍛ㄦ湡涓2蟺銆傛鍓叉槸涓夎鍑芥暟鐨勬鍑芥暟锛姝ｅ鸡...
绛旓細3 cos2x=2sin锛2x+ 蟺 3 锛夊皢鍑芥暟y=2sinx鐨勫浘璞″悜宸﹀钩绉 蟺 3 涓崟浣嶏紝鍐嶄繚鎸佸浘璞′笂鍚勭偣绾靛潗鏍囦笉鍙橈紝妯潗鏍囧彉涓哄師鏉ョ殑 1 2 锛屽彲寰楀埌鍑芥暟f锛坸锛=2sin锛2x+ 蟺 3 锛夌殑鍥捐薄锛堟垨灏嗗嚱鏁皔=2sinx鐨勫浘璞′笂鍚勭偣淇濇寔绾靛潗鏍囦笉鍙橈紝妯潗鏍囧彉涓哄師鏉ョ殑 ...
绛旓細1+sin(a) =(sin +cos )2 1-sin(a) = (sin -cos )2 鍏朵粬闈為噸鐐逛笁瑙鍑芥暟 csc(a) = sec(a) = 鍙屾洸鍑芥暟 sinh(a)= cosh(a)= tg h(a)= 鍏紡涓锛氳伪涓轰换鎰忚锛岀粓杈圭浉鍚岀殑瑙掔殑鍚屼竴涓夎鍑芥暟鐨勫肩浉绛夛細sin锛2k蟺锛嬑憋級= sin伪 cos锛2k蟺锛嬑锛= cos伪 tan锛2k蟺锛嬑憋級= tan...
绛旓細y 锛sin锛坸锛嬒/3锛塻in锛坸锛嬒/2锛锛濓紞锛籹inxcos锛埾/3锛夛紜cosxsin锛埾/3锛夛冀cosx 锛濓紞锛1/2锛塻inxcosx锛嶏紙鈭3/2锛夛紙cosx锛^2锛濓紞锛1/4锛塻in2x锛嶏紙鈭3/4锛夛紙1锛媍os2x锛夛紳锛1锛嶏紙1/4锛塻in2x锛嶏紙鈭3/4锛塩os2x锛濓紞1锛嶏紙1/2锛夛蓟sin2xcos锛埾/3锛夛紜cos2xsin锛埾/3锛夛冀...
绛旓細125t-9.25)(SI)$x2涓巟1涓ゅ璐ㄥ厓闂寸殑鎸姩鍒濈浉鍒嗗埆涓合1=-3.7rad銆佅2=-9.25rad锛屽垯浜岃呯殑鐩镐綅宸负 鈻诚=蠄2-蠄1=-9.25-(-3.7)=-5.55rad$灏唗=4s锛寈1=10m浠ｅ叆娉鍑芥暟y=0.25cos(125t-0.37x)涓紝鍒欏綋t=4s鏃讹紝x1澶勮川鍏冪殑鎸姩浣嶇Щ涓 y=0.25cos(125脳4-3.7)=0.25(m)
绛旓細鍏充簬璇卞鍏紡锛屾墍鏈夌殑鍏紡閮藉彲浠ュ綊绾充负锛氬鍙樺伓涓嶅彉锛岀鍙风湅璞￠檺銆傚鍙樺伓涓嶅彉锛氬嵆鐪嬒/2鍓嶇殑绯绘暟鏄鏁拌繕鏄伓鏁帮紝濡傛灉鏄伓鏁帮紝閭ｄ箞鍑芥暟鍚嶄笉鍙橈紝濡傛灉鏄鏁帮紝鍙樻垚瀹冪殑浣欏悕鍑芥暟锛宻in(3蟺/2+a)锛3鏄鏁版墍浠ュ彉涓cos锛屽張濡俢ot(蟺+a),蟺=2*蟺/2锛2鏄伓鏁版墍浠ヤ笉鍙橈紝鍑芥暟鍚嶄粛涓篶ot銆
绛旓細cos(A-B) = cosAcosB+sinAsinB tan(A+B) = (tanA+tanB)/(1-tanAtanB)tan(A-B) = (tanA-tanB)/(1+tanAtanB)cot(A+B) = (cotAcotB-1)/(cotB+cotA) �cot(A-B) = (cotAcotB+1)/(cotB-cotA)[缂栬緫鏈]鍊嶈鍏紡 Sin2A=2SinA•CosA Cos2A=CosA^2-SinA^2=...
绛旓細y=2pt 褰撴棆杞n=45鏃 x'=2pt²cos45+2ptsin45=(鏍瑰彿2)pt²+pt y'=-2pt²sin45+2ptcos45=(-鏍瑰彿2)pt²+pt 涓ゅ紡鐩稿姞寰 x'+y'=2pt 涓ゅ紡鐩稿噺寰 x'-y'=2(鏍瑰彿2)pt²鎵浠ユ湁锛(x'+y')²=(鏍瑰彿2)p(x'-y')杩欐槸鏃嬭浆鍚庣殑鎶涚墿绾跨殑鏂圭▼ 鍙浠=...
绛旓細cosx+cosy=2cos((x+y)/2)*cos((x-y)/2)cosx-cosy=-2sin((x+y)/2)*sin((x-y)/2)5.3 鍊嶈鍏紡 sin锛3a)鈫3sina-4sin^3a =sin(a+2a)=sin2acosa+cos2asina =2sina锛1-sin^2a)+锛1-2sin^2a)sina =3sina-4sin^3a cos3a鈫掞紙2cos^2a-1锛塩osa-2锛1-cos^2a)cosa =...
