根号3sinx-cosx咋化简? 根号(3sinx+cosx)怎么化简?
\u6839\u53f73sinx+cosx\u5982\u4f55\u5316\u7b80\u89e3\u221a3sinx+cosx
=2\uff08\u221a3/2sinx+1/2cosx\uff09
=2\uff08cos\u03c0/6sinx+sin\u03c0/6cosx\uff09
=2sin\uff08x+\u03c0/6)
\u6839\u53f7\uff083sinx+cosx\uff09
=\u6839\u53f7[\u6839\u53f7\uff083^2+1^2\uff09\uff083/(\u6839\u53f73^2+1^2)\uff09sinx+1/(\u6839\u53f73^2+1^2)cosx]
=\u6839\u53f7[\u6839\u53f710\uff08\uff083/\u6839\u53f710\uff09sinx+1/\u6839\u53f710cosx\uff09]
\u4ee43/\u6839\u53f710=cos\u03b1\uff0c1/\u6839\u53f710=sin\u03b1 \u5219tan\u03b1=1/3
\u539f\u5f0f=\u6839\u53f7\uff08\u6839\u53f710sin(x+\u03b1)\uff09=10\u6839\u53f7\uff08sin\uff08x+\u03b1\uff09
=2(sinxcosπ/6-cosxsinπ/6)
=2sin(x-π/6)
绛旓細鈭3sinx-cosx =2(sinxcos蟺/6-cosxsin蟺/6)=2sin(x-蟺/6)
绛旓細3sinx-cosx =鈭10sin(x+胃)鍏朵腑tan胃=-1/3
绛旓細3sinx-cosx=2a-3 鈭10锛坰inx脳3鈭10/10-cosx脳鈭10/10锛=2a-3 璁綾os涔=3鈭10/10锛宻in涔=鈭10/10 鈭粹垰10sin锛坸-涔勶級=2a-3 sin锛坸-涔勶級=锛2a-3锛/鈭10 鈭-1鈮わ紙2a-3锛/鈭10鈮1 瑙ｅ緱锛3-鈭10锛/2鈮鈮わ紙3+鈭10锛/2 ...
绛旓細= 2 * ( (鏍瑰彿3)/2 * sinx - 1/2 * cosx)= 2 * (sinxcos蟺/6 - cosxsin蟺/6)= 2 * sin(x - 蟺/6)鍥犱负0
绛旓細杩欐槸涓夎鍑芥暟鐨勫簲鐢ㄤ腑鐨勫父瑙侀鍨嬨傝鎯呭鍥炬墍绀:渚涘弬鑰冿紝璇风瑧绾炽
绛旓細瑙ｇ敱f(x)=鈭3sinx-cosx=2(鈭3/2sinx-1/2cosx)=2sin(x-蟺/6)鏁呭嚱鏁扮殑鍛ㄦ湡T=2蟺褰2k蟺-蟺/2鈮-蟺/6鈮2k蟺+蟺/2,k灞炰簬Z,y鏄鍑芥暟,鍗2k蟺-蟺/3鈮鈮2k蟺+2蟺/3,k灞炰簬Z,y鏄鍑芥暟,鏁呭嚱鏁扮殑澧炲尯闂翠负[2k蟺-蟺/3,2k蟺+2蟺/3],k灞炰簬Z.
绛旓細f(x)=鈭3sinx-cosx=2(鈭3/2sinx-1/2cosx)=2(sinxcos谢/6-sin谢/6cosx)=2sin(x-谢/6)2k谢-谢/2 鈮-谢/6< 2k谢+谢/2 x鈭圼2k谢-谢/3,2k谢-2谢/3)锛屽嚱鏁癴(x)=2sin(x-谢/6)鍗曡皟閫掑锛庢墍浠ュ嚱鏁癴(x)鐨勫崟璋冮掑鍖洪棿鏄痆2k谢-谢/3,2k谢-2谢/3)...
绛旓細鈭3sinx-cosx=1 2[(鈭3/2)sinx-cosx(1/2)]=1 2[sinxcos(蟺/6)-cosxsin(蟺/6)]=1 sin(x-蟺/6)=1/2 0<x<蟺 -蟺/6<x-蟺/6<5蟺/6 x-蟺/6=蟺/6 x=蟺/3
绛旓細y=鈭3sinx-cosx=2锛(鈭3/2)sinx-(1/2)cosx锛=2sin(x-蟺/6)鍗冲緱鍛ㄦ湡T=2蟺.鏈澶у间负2鏈灏忓间负-2
绛旓細1 y=鏍瑰彿3 sinx-cosx鍦▁鈭堛0锛屽厐銆戠殑鏈灏忓间负 f(x)=鈭3sinx-cosx=2sin(x-30掳),x鈭圼0锛180掳],X-30掳鈭圼-30掳,150掳]锛屾墍浠ュ綋x-30掳=-30掳锛寈=0掳鏃讹紝2sin(x-30掳)鍙栧緱鏈灏忓硷紝涓-1銆2 x鈭堬紙0掳锛90掳锛夛紝sinx=3/5锛屾眰sin锛坸- 鍏/6锛夊洜涓簒鏄攼瑙掞紝鎵浠osx=4/...
