求高人赐教高中阶段所有正弦余弦的公式(本人文科生) 求高中有关正弦余弦函数的公式
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\u4f59\u5f26\u5b9a\u7406\u662f\u63ed\u793a\u4e09\u89d2\u5f62\u8fb9\u89d2\u5173\u7cfb\u7684\u91cd\u8981\u5b9a\u7406\uff0c\u76f4\u63a5\u8fd0\u7528\u5b83\u53ef\u89e3\u51b3\u4e00\u7c7b\u5df2\u77e5\u4e09\u89d2\u5f62\u4e24\u8fb9\u53ca\u5939\u89d2\u6c42\u7b2c\u4e09\u8fb9\u6216\u8005\u662f\u5df2\u77e5\u4e09\u4e2a\u8fb9\u6c42\u4e09\u89d2\u7684\u95ee\u9898\uff0c\u82e5\u5bf9\u4f59\u5f26\u5b9a\u7406\u52a0\u4ee5\u53d8\u5f62\u5e76\u9002\u5f53\u79fb\u4e8e\u5176\u5b83\u77e5\u8bc6\uff0c\u5219\u4f7f\u7528\u8d77\u6765\u66f4\u4e3a\u65b9\u4fbf\u3001\u7075\u6d3b\u3002cos A=(b²+c²-a²)/2bc
\u6269\u5c55\u8d44\u6599\uff1a
\u5728\u25b3ABC\u4e2d\uff0c
sin²A+sin²B-sin²C
=[1-cos\uff082A\uff09]/2+[1-cos\uff082B\uff09]/2-[1-cos\uff082C\uff09]/2\uff08\u964d\u5e42\u516c\u5f0f\uff09
=-[cos\uff082A\uff09+cos\uff082B\uff09]/2+1/2+1/2-1/2+[cos\uff082C\uff09]/2
=-cos\uff08A+B\uff09cos\uff08A-B\uff09+[1+cos\uff082C\uff09]/2\uff08\u548c\u5dee\u5316\u79ef\uff09
=-cos\uff08A+B\uff09cos\uff08A-B\uff09+cos²C\uff08\u964d\u5e42\u516c\u5f0f\uff09
=cosC*cos\uff08A-B\uff09-cosC*cos\uff08A+B\uff09\uff08\u2220A+\u2220B=180\u00b0-\u2220C\u4ee5\u53ca\u8bf1\u5bfc\u516c\u5f0f\uff09
=cosC[cos(A-B)-cos\uff08A+B\uff09]
=2cosC*sinA*sinB\uff08\u548c\u5dee\u5316\u79ef\uff09\uff08\u7531\u6b64\u8bc1\u660e\u4f59\u5f26\u5b9a\u7406\u89d2\u5143\u5f62\u5f0f\uff09
\u8bbe\u25b3ABC\u7684\u5916\u63a5\u5706\u534a\u5f84\u4e3aR
\u2234\uff08RsinA\uff09²+\uff08RsinB\uff09²-\uff08RsinC\uff09²=2\uff08RsinA\uff09*\uff08RsinB\uff09*cosC
\u2234a²+b²-c²=2ab*cosC\uff08\u6b63\u5f26\u5b9a\u7406\uff09
\u2234c²=a²+b²-2ab*cosC
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1.\u8bf1\u5bfc\u516c\u5f0f
sin(-a)=-sin(a)
cos(-a)=cos(a)
sin(2\u03c0-a)=cos(a)
cos(2\u03c0-a)=sin(a)
sin(2\u03c0+a)=cos(a)
cos(2\u03c0+a)=-sin(a)
sin(\u03c0-a)=sin(a)
cos(\u03c0-a)=-cos(a)
sin(\u03c0+a)=-sin(a)
cos(\u03c0+a)=-cos(a)
tgA=tanA=sinAcosA
2.\u4e24\u89d2\u548c\u4e0e\u5dee\u7684\u4e09\u89d2\u51fd\u6570
sin(a+b)=sin(a)cos(b)+cos(\u03b1)sin(b)
cos(a+b)=cos(a)cos(b)-sin(a)sin(b)
sin(a-b)=sin(a)cos(b)-cos(a)sin(b)
cos(a-b)=cos(a)cos(b)+sin(a)sin(b)
tan(a+b)=tan(a)+tan(b)1-tan(a)tan(b)
tan(a-b)=tan(a)-tan(b)1+tan(a)tan(b)
3.\u548c\u5dee\u5316\u79ef\u516c\u5f0f
sin(a)+sin(b)=2sin(a+b2)cos(a-b2)
sin(a)−sin(b)=2cos(a+b2)sin(a-b2)
cos(a)+cos(b)=2cos(a+b2)cos(a-b2)
cos(a)-cos(b)=-2sin(a+b2)sin(a-b2)
4.\u79ef\u5316\u548c\u5dee\u516c\u5f0f (\u4e0a\u9762\u516c\u5f0f\u53cd\u8fc7\u6765\u5c31\u5f97\u5230\u4e86)
sin(a)sin(b)=-12⋅[cos(a+b)-cos(a-b)]
cos(a)cos(b)=12⋅[cos(a+b)+cos(a-b)]
sin(a)cos(b)=12⋅[sin(a+b)+sin(a-b)]
5.\u4e8c\u500d\u89d2\u516c\u5f0f
sin(2a)=2sin(a)cos(a)
cos(2a)=cos2(a)-sin2(a)=2cos2(a)-1=1-2sin2(a)
6.\u534a\u89d2\u516c\u5f0f
sin2(a2)=1-cos(a)2
cos2(a2)=1+cos(a)2
tan(a2)=1-cos(a)sin(a)=sina1+cos(a)
7.\u4e07\u80fd\u516c\u5f0f
sin(a)=2tan(a2)1+tan2(a2)
cos(a)=1-tan2(a2)1+tan2(a2)
tan(a)=2tan(a2)1-tan2(a2)
8.\u5176\u5b83\u516c\u5f0f(\u63a8\u5bfc\u51fa\u6765\u7684 )
a⋅sin(a)+b⋅cos(a)=a2+b2sin(a+c) \u5176\u4e2d tan(c)=ba
a⋅sin(a)-b⋅cos(a)=a2+b2cos(a-c) \u5176\u4e2d tan(c)=ab
1+sin(a)=(sin(a2)+cos(a2))2
1-sin(a)=(sin(a2)-cos(a2))2
csc(a)=1sin(a)
sec(a)=1cos(a)
对于任意三角形 三边为a,b,c 三角为A,B,C 满足性质
(注：a*b、a*c就是a乘b、a乘c 。a^2、b^2、c^2就是a的平方，b的平方，c的平方。)
a^2=b^2+c^2-2*b*c*CosA
b^2=a^2+c^2-2*a*c*CosB
c^2=a^2+b^2-2*a*b*CosC
CosC=(a^2+b^2-c^2)/2ab
CosB=(a^2+c^2-b^2)/2ac
CosA=(c^2+b^2-a^2)/2bc
正弦定理
即a/sinA=b/sinB=c/sinC=2R（2R在同一个三角形中是恒量，是此三角形外接圆的半径的两倍）
(1) a=2RsinA, b=2RsinB, c=2RsinC;
(2) sinA : sinB : sinC = a : b : c;
两角和公式sin(a+b)=sinacosb+cosasinbsin(a-b)=sinacosb-sinbcosa
cos(a+b)=cosacosb-sinasinbcos(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)
倍角公式tan2a=2tana/[1-(tana)^2]
cos2a=(cosa)^2-(sina)^2=2(cosa)^2 -1=1-2(sina)^2
sin2a=2sina*cosa
半角公式sin(a/2)=√((1-cosa)/2)
sin(a/2)=-√((1-cosa)/2)cos(a/2)=√((1+cosa)/2)
cos(a/2)=-√((1+cosa)/2)tan(a/2)=√((1-cosa)/((1+cosa))
tan(a/2)=-√((1-cosa)/((1+cosa))cot(a/2)=√((1+cosa)/((1-cosa))
tan(a/2)=(1-cosa)/sina=sina/(1+cosa)
诱导公式sin(-a)=-sin(a)
cos(-a)=cos(a)
sin(pi/2-a)=cos(a)
cos(pi/2-a)=sin(a)
sin(pi/2+a)=cos(a)
cos(pi/2+a)=-sin(a)
sin(pi-a)=sin(a)
cos(pi-a)=-cos(a)
sin(pi+a)=-sin(a)
cos(pi+a)=-cos(a)
tana=sina/cosa
万能公式sin(a)= (2tan(a/2))/(1+tan^2(a/2))
cos(a)= (1-tan^2(a/2))/(1+tan^2(a/2))
tan(a)= (2tan(a/2))/(1-tan^2(a/2))
其它公式a*sin(a)+b*cos(a)=sqrt(a^2+b^2)sin(a+c) [其中，tan(c)=b/a]
a*sin(a)-b*cos(a)=sqrt(a^2+b^2)cos(a-c) [其中，tan(c)=a/b]1+sin(a)=(sin(a/2)+cos(a/2))^21-sin(a)=(sin(a/2)-cos(a/2))^2
余弦函数是一个偶函数啊,f(x)=f(-x).它是关于Y轴对称的
因为余弦函数是一个偶函数啊,f(x)=f(-x).它是关于Y轴对称的昂```
你把它的图象画出来你就全清楚了``
这样啊,我这已经很通俗了.那你在以后肯定会学到,你现在就先记住吧,不用迷茫了``
以后就懂了`
余弦定理
对于任意三角形 三边为a,b,c 三角为A,B,C 满足性质
(注：a*b、a*c就是a乘b、a乘c 。a^2、b^2、c^2就是a的平方，b的平方，c的平方。)
a^2=b^2+c^2-2*b*c*CosA
b^2=a^2+c^2-2*a*c*CosB
c^2=a^2+b^2-2*a*b*CosC
CosC=(a^2+b^2-c^2)/2ab
CosB=(a^2+c^2-b^2)/2ac
CosA=(c^2+b^2-a^2)/2bc
正弦定理
即a/sinA=b/sinB=c/sinC=2R（2R在同一个三角形中是恒量，是此三角形外接圆的半径的两倍）
(1) a=2RsinA, b=2RsinB, c=2RsinC;
(2) sinA : sinB : sinC = a : b : c;
两角和公式sin(a+b)=sinacosb+cosasinbsin(a-b)=sinacosb-sinbcosa
cos(a+b)=cosacosb-sinasinbcos(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)
倍角公式tan2a=2tana/[1-(tana)^2]
cos2a=(cosa)^2-(sina)^2=2(cosa)^2 -1=1-2(sina)^2
sin2a=2sina*cosa
半角公式sin(a/2)=√((1-cosa)/2)
sin(a/2)=-√((1-cosa)/2)cos(a/2)=√((1+cosa)/2)
cos(a/2)=-√((1+cosa)/2)tan(a/2)=√((1-cosa)/((1+cosa))
tan(a/2)=-√((1-cosa)/((1+cosa))cot(a/2)=√((1+cosa)/((1-cosa))
tan(a/2)=(1-cosa)/sina=sina/(1+cosa)
诱导公式sin(-a)=-sin(a)
cos(-a)=cos(a)
sin(pi/2-a)=cos(a)
cos(pi/2-a)=sin(a)
sin(pi/2+a)=cos(a)
cos(pi/2+a)=-sin(a)
sin(pi-a)=sin(a)
cos(pi-a)=-cos(a)
sin(pi+a)=-sin(a)
cos(pi+a)=-cos(a)
tana=sina/cosa
万能公式sin(a)= (2tan(a/2))/(1+tan^2(a/2))
cos(a)= (1-tan^2(a/2))/(1+tan^2(a/2))
tan(a)= (2tan(a/2))/(1-tan^2(a/2))
其它公式a*sin(a)+b*cos(a)=sqrt(a^2+b^2)sin(a+c) [其中，tan(c)=b/a]
a*sin(a)-b*cos(a)=sqrt(a^2+b^2)cos(a-c) [其中，tan(c)=a/b]1+sin(a)=(sin(a/2)+cos(a/2))^21-sin(a)=(sin(a/2)-cos(a/2))^2
绛旓細姝ｅ鸡:a/sinA=b/sinB=c/sinC=2R a,b,c涓轰笁瑙掑舰鐨勪笁杈,A,B,C涓轰笁杈圭殑瀵硅.R涓轰笁瑙掑舰澶栨帴鍦嗙殑鍗婂緞.鍙樺舰:涓夎褰㈤潰绉疭=1/2 *absinC=1/2 *acsinB=1/2 *bcsinA 浣欏鸡:a^2=b^2+c^2-2bccosA b^2=a^2+c^2-2accosB c^2=a^2+b^2-2abcosC 鍙樺舰:cosA=(b^2+c^2-a^2)/(...
绛旓細鎵鏈夋浣欏鸡鍏紡濡備笅锛1. 姝ｅ鸡鍏紡锛氭寮﹀拰宸叕寮忥細sin = sinAcosB + cosAsinB锛泂in = sinAcosB - cosAsinB銆傛寮﹀嶈鍏紡锛歴in2A = 2sinAcosA銆傛寮﹀崐瑙掑叕寮忥細sin = 鈭歔/2]銆傛寮︾殑鍜屼笌宸浆鍖栧叕寮忥細cos = sinA銆傜敱姝ゅ叕寮忓彲鐭ヤ綑寮︿篃鍙互杞崲涓烘寮﹀嚱鏁般傛寮﹀叕寮忔弿杩颁簡鍦ㄤ竴涓洿瑙掍笁瑙掑舰涓紝涓涓...
绛旓細1. 姝ｅ鸡瀹氱悊:A / Sina = B / SINB = C / sinc = 2R銆2. 浣欏鸡瀹氱悊:cos a = (b²+ c²- a²)/ 2bc銆3.姝ｅ鸡浣欏鸡瀹氱悊鏄寚姝ｅ鸡瀹氱悊鍜屼綑寮﹀畾鐞嗐傚畠鏄彮绀轰笁瑙掑舰杈逛笌瑙掍箣闂村叧绯荤殑涓涓噸瑕佸畾鐞嗐傚畠鍙互鐩存帴鐢ㄤ簬姹傝В涓夎褰㈤棶棰樸傚鏋滃皢浣欏鸡瀹氱悊杩涜鍙樺舰锛屽苟閫傚綋鍦拌浆绉诲埌鍏朵粬鐭ヨ瘑...
绛旓細瑙ｏ細锛1锛夊洜涓篶osC=2鈭5/5>0锛屾墍浠ヤ负閿愯銆俿inC=鈭氾紙1-cosC²锛=鈭5/5.sinA=sin(蟺-(B+C))=sin(B+C)=(sinBcosC+cosBsinC锛=鈭2(2鈭5/5+鈭5/5)/2=3鈭10/10.(2)鐢姝ｅ鸡瀹氱悊锛欱C=ACsinA/sinB=6. CD=3 鐢浣欏鸡瀹氱悊锛欰D=鈭氾紙AC²+CD²-2*AC*CD*cosC锛=鈭...
绛旓細鐗规畩瑙掔殑鍊煎涓嬭〃锛氬湪鐩磋涓夎褰腑锛屼换鎰忎竴閿愯鈭燗鐨勫杈逛笌鏂滆竟鐨勬瘮鍙仛鈭燗鐨姝ｅ鸡锛岃浣渟inA锛堢敱鑻辫sine涓璇嶇畝鍐欏緱鏉ワ級锛屽嵆sinA=鈭燗鐨勫杈/鏂滆竟銆
绛旓細鈶犺В锛氱敱A锛婤锛婥锛180搴︼紝A+C=2B锛屽彲寰 3B锛180搴 B锛60搴 鏍规嵁姝ｅ鸡瀹氱悊锛屽彲寰 a/sinA=b/sinB 1/sinA=鈭3/sin60 sinA=鈭3/2/鈭3=1/2 鈶¤В锛歝os(A-C)+cosB =cos(A-C)-cos(A+C)=cosAcosC+sinAsinC-cosAcosC+sinAsinC =2sinAsinC=3/2 sinAsinC=3/4 鏍规嵁姝ｅ鸡瀹氱悊锛宎/sinA...
绛旓細sin伪=- sin(-伪) sin伪=sin(蟺-伪)=-sin(蟺+伪) sin伪=cos(蟺/2-伪) sin2伪=2*sin伪*cos伪 sin²伪=(1-cos2伪)*1/2 cos伪=cos(-伪) cos伪=-cos(蟺-伪)=-cos(蟺+伪) cos伪=sin(蟺/2-伪) cos2伪=2cos²伪-1=1-2sin²伪=cos&#...
绛旓細姝ｅ鸡瀹氱悊锛圱he Law of Sines锛夋槸涓夎瀛︿腑鐨勪竴涓熀鏈畾鐞嗭紝瀹冩寚鍑衡滃湪浠绘剰涓涓钩闈笁瑙掑舰涓紝鍚勮竟鍜屽畠鎵瀵硅鐨勬寮﹀肩殑姣旂浉绛変笖绛変簬澶栨帴鍦嗙殑鐩村緞鈥濓紝鍗砤/sinA=b/sinB=c/sinC= 2r=D锛坮涓哄鎺ュ渾鍗婂緞锛孌涓虹洿寰勶級銆浣欏鸡瀹氱悊锛屾姘忓钩闈㈠嚑浣曞鍩烘湰瀹氱悊銆備綑寮﹀畾鐞嗘槸鎻忚堪涓夎褰腑涓夎竟闀垮害涓庝竴涓鐨勪綑寮...
绛旓細姝ｅ鸡瀹氱悊锛圱he Law of Sines锛夋槸涓夎瀛︿腑鐨勪竴涓熀鏈畾鐞嗭紝瀹冩寚鍑衡滃湪浠绘剰涓涓钩闈笁瑙掑舰涓紝鍚勮竟鍜屽畠鎵瀵硅鐨勬寮﹀肩殑姣旂浉绛変笖绛変簬澶栨帴鍦嗙殑鐩村緞鈥濓紝鍗砤/sinA=b/sinB=c/sinC= 2r=D锛坮涓哄鎺ュ渾鍗婂緞锛孌涓虹洿寰勶級銆浣欏鸡瀹氱悊锛屾姘忓钩闈㈠嚑浣曞鍩烘湰瀹氱悊銆備綑寮﹀畾鐞嗘槸鎻忚堪涓夎褰腑涓夎竟闀垮害涓庝竴涓鐨勪綑寮...
绛旓細1. A=30搴.鍥犱负 sinB+cosB=鏍瑰彿2锛岃 (sinB)^2+(cosB)^2=1锛岀敱姝ゅ彲浠ヨВ鍑 sinB=cosB=鏍瑰彿2/2锛屽洜姝ゅ繀鏈 B=45搴. 鐢姝ｅ鸡瀹氱悊锛歛/sinA=b/sinB=2/(鏍瑰彿2/2)锛屼笖 a=鏍瑰彿2锛屾墍浠 sinA=1/2. 鍙 a<b锛屾墍浠 A<B锛屼粠鑰屽彧鑳芥湁 A=30搴︺2. 鏍瑰彿3/2.寤堕暱AD鑷矱浣垮緱 DE=AD. 瀹规槗...
