tan在(0,2π)变化规律 若方程tan（2x+π3）=33，则该方程在区间[0，2π）...
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\u7531tan\uff082x+\u03c03\uff09=33\uff0c\u5f972x+\u03c03=k\u03c0+\u03c06\uff0c\u5373x=k\u03c02-\u03c012\uff0c\u75310\u2264k\u03c02-\u03c012\uff1c2\u03c0\uff0c\u89e3\u5f9716\u2264k\uff1c4+16\uff0c\u2235k\u2208Z\uff0c\u2234k=1\uff0c2\uff0c3\uff0c4\uff0c\u6545\u65b9\u7a0b\u5728\u533a\u95f4[0\uff0c2\u03c0\uff09\u89e3\u7684\u4e2a\u6570\u4e3a4\u4e2a\uff0e\u6545\u7b54\u6848\u4e3a\uff1a4
tanx是以π为最小正周期的周期函数，在（0,2π）上分为三段。在（0，π/2）上单调递增，值域为（0，+∞）。（π/2,3π/2）上单调递增，值域为（—∞，+∞）。（3π/2,2π）上单调递增，值域为（-∞，0）。（0，π/2）上单增
（π/2,3π/2）上单增
（3π/2,2π）上单增
分段函数，分上面三段
绛旓細tanx鏄互蟺涓烘渶灏忔鍛ㄦ湡鐨勫懆鏈熷嚱鏁帮紝鍦紙0,2蟺锛涓婂垎涓轰笁娈点傚湪锛0锛屜/2锛変笂鍗曡皟閫掑锛屽煎煙涓猴紙0锛+鈭烇級銆傦紙蟺/2,3蟺/2锛変笂鍗曡皟閫掑锛屽煎煙涓猴紙鈥斺垶锛+鈭烇級銆傦紙3蟺/2,2蟺锛変笂鍗曡皟閫掑锛屽煎煙涓猴紙-鈭烇紝0锛夈
绛旓細tan(2x+蟺/3)鐨勫懆鏈熸槸蟺/4 鑰宼an(2x+蟺/3)鍦ㄤ竴涓懆鏈熷唴鏄崟澧炲嚱鏁 鍥犳鍦ㄥ尯闂淬0,2蟺銆戜笂鏈夊洓涓懆鏈,鏈夊洓涓В
绛旓細鍒欐湁锛歴in伪-cos伪<0 鈭2sin(伪-蟺/4)<0 sin(伪-蟺/4)<0 鐢变簬锛毼卞睘浜(0,2蟺)鍒欙細伪-蟺/4灞炰簬(-蟺/4,7蟺/4)鍙堬細sin(伪-蟺/4)<0 鍒欙細伪-蟺/4灞炰簬(-蟺/4,0)U(蟺,7蟺/4)鍒欙細伪灞炰簬(0,蟺/4)U(5蟺/4,2蟺)鐢变簬锛tan伪>cot伪 鍒欙細tan伪-cot伪>0 tan伪-1/tan伪...
绛旓細=tan²x锛0 鎵浠(x)鍦╗0锛屜/2)涓婂崟璋冮掑锛屾墍浠ワ紝褰搙鈭(0锛屜/2)鏃 f(x)锛瀎(0)=0 鍗筹細tanx锛瀤
绛旓細0锛渪锛溝 y= tanx 鍗曡皟澧炲尯闂淬0锛屜/2)鍗曡皟澧炲尯闂锛埾/2锛屜銆
绛旓細鎺ョ潃锛屾垜浠墿灞曡繖涓閲庯紝瑙傚療 cos胃 鐨勫浘鍍忋備笌sin胃涓嶅悓锛宑os胃鐨勫浘褰㈡槸鍋跺嚱鏁帮紝瀵圭О浜巠杞达紝鑰屽畠鐨勫懆鏈熷悓鏍疯鐩栨暣涓疄鏁拌酱銆傚綋胃鍦0鍜蟺/2涔嬮棿鍙樺寲鏃讹紝cos胃鍛堢幇鍑轰粠1閫掑噺鍒0鐨瑙勫緥锛杩欎负鍚庣画鐨勫掓暟杩愮畻鎻愪緵浜嗗熀纭銆Tan胃 鐨勫浘鍍忓垯鏇翠负鏈夎叮锛屾垜浠仛鐒﹀湪瀹冪殑瀹氫箟鍩-蟺/2鍒跋/2銆tan胃鐨勫鍋...
绛旓細tanx - x 鐨勭粨鏋滀篃鍦鍙樺寲锛鍥犳鍙互鏋勯犱竴涓嚱鏁版潵浣滃嚭鍒ゆ柇銆備护 f(x) = tanx -x 瀵逛笂闈㈢殑鍑芥暟姹傚 f鈥(x) = 1/cos^2 x -1 =( 1-cos^2 x)/cos^2x = sin^2 x/cos^2 x = tan^2 x > 0 杩欒鏄庯紝鍑芥暟鍦ㄥ叾瀹氫箟鍖洪棿鍗曡皟閫掑锛岃 f锛0锛锛tan0 - 0 = 0 鑰宖(x)鐨勫畾涔夊尯闂...
绛旓細涓夎鍑芥暟tan鍏紡鏈夊涓嬶細鍊掓暟鍏崇郴锛歵an伪路cot伪锛1 sin伪路csc伪锛1 cos伪路sec伪锛1 鍟嗙殑鍏崇郴锛歴in伪锛廲os伪锛漷an伪锛漵ec伪锛廲sc伪 cos伪锛弒in伪锛漜ot伪锛漜sc伪锛弒ec伪 骞虫柟鍏崇郴锛歴in^2(伪锛+cos^2(伪锛=1 1+tan^2(伪锛=sec^2(伪锛1+cot^2(伪锛=csc^2(伪锛夊湪鐩磋鍧愭爣绯讳腑锛...
绛旓細杩欎釜鏄笉鍙Н鐨勶紝tanx鐨勫師鍑芥暟鏄-lncosx +C锛岃岃鍑芥暟鍦▁瓒嬩簬鏃犵┓澶ф椂涓嶆敹鏁涖備护sint=2^(1/2)*sinx鍒檛鈭圼0,蟺/2] costdt=2^(1/2)cosxdx dx=2^(1/2)*1/2*costdt/[1-1/2*(sint)^2]^(1/2)鍘熺Н鍒=2^(1/2)*鈭(cost)^2/dt/[1-1/2*(sint)^2]^(1/2) 鏈夌Н鍒嗗尯闂碵...
绛旓細璁惧畾鍑芥暟鍦╗0,2r]鍖洪棿鍐呯殑鍙樺寲瑙勫緥锛屽彲浠ラ氳繃鍙樺寲鐨勬尟骞呫佽棰戠巼鍜岀浉浣嶆潵纭畾銆傚叿浣撳舰寮忓彲浠ヨ〃绀轰负锛歠(x) = A * sin(2蟺/2r * x + 蠁)鍏朵腑锛孉琛ㄧず鎸箙锛堝嚱鏁板肩殑鏈澶у彉鍖栬窛绂伙級锛屜嗚〃绀虹浉浣嶏紙鍑芥暟鍊肩殑鍋忕Щ閲忥紝鍗冲湪x=0鏃剁殑鍑芥暟鍊硷級銆傝繖鏍锋瀯閫犵殑鍑芥暟鍦ㄥ尯闂碵0,2r]鍐呭叿鏈夊懆鏈熸у彉鍖栵紝骞朵笖...
