关于三角函数诱导公式的题。 高中数学三角函数关于诱导公式方面的例题，越多越好，我会加分的
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A. B. C. 2 D. 4
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1\u3001tan600\u00b0\u7684\u503c\u662f\uff08 \uff09
\uff08A\uff09 \uff08B\uff09 \uff08C\uff09 (D)
2\u3001\u51fd\u6570y\uff1dsin(2x\uff0b )\u7684\u6700\u5c0f\u6b63\u5468\u671f\u662f( )
(A) (B) (C) 2 (D) 4
3\u3001\u201c\u7b49\u5f0f \u6210\u7acb\u201d\u662f\u201c \u6210\u7b49\u5dee\u6570\u5217\u201d\u7684\uff08 \uff09
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4\u3001\u5f53 \u7684\u503c\u57df\u662f\uff08 \uff09
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5\u3001\u82e5 \u7684\u5947\u51fd\u6570\uff0c\u5219 \u53ef\u4ee5\u662f\uff08 \uff09
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6\u3001\u5c06\u51fd\u6570 \u7684\u56fe\u8c61\u6309\u5411\u91cf \u5e73\u79fb\uff0c\u5e73\u79fb\u540e\u7684\u56fe\u8c61\u5982\u56fe\u6240\u793a\uff0c\u5219\u5e73\u79fb\u540e\u7684\u56fe\u8c61\u6240\u5bf9\u5e94\u51fd\u6570\u7684\u89e3\u6790\u5f0f\u662f\uff08 \uff09
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7\u3001\u82e5\u25b3ABC\u9762\u79efS= \u5219\u2220C=\uff08 \uff09
\uff08A\uff09 \uff08B\uff09 \uff08C\uff09 \uff08D\uff09
8\u3001\u5728 \u4e2d\uff0c\u82e5 \uff0c\u5219 \u4e00\u5b9a\u662f\uff08 \uff09
\uff08A\uff09\u7b49\u8170\u4e09\u89d2\u5f62 \uff08B\uff09\u76f4\u89d2\u4e09\u89d2\u5f62 \uff08C\uff09\u7b49\u8170\u76f4\u89d2\u4e09\u89d2\u5f62 \uff08D\uff09\u7b49\u8170\u6216\u76f4\u89d2\u4e09\u89d2\u5f62
9\u3001 \u5219 \u7684\u6700\u5927\u503c\u548c\u6700\u5c0f\u503c\u5206\u522b\u662f\uff08 \uff09
\uff08A\uff097\u30015 \uff08B\uff097\u3001\uff0d \uff08C\uff095\u3001\uff0d \uff08D\uff097\u3001\uff0d5
10\uff0e\u5df2\u77e5\u5411\u91cf \u5219 \u4e0e \u7684\u5939\u89d2\u4e3a\uff08 \uff09
\uff08A\uff09 \uff08B\uff09 \uff08C\uff09 \uff08D\uff09
\u4e8c\u3001\u586b\u7a7a\u9898\uff08\u672c\u5927\u9898\u51714\u5c0f\u9898\uff0c\u6bcf\u5c0f\u98985\u5206\uff0c\u517120\u5206\uff09
11. \u5982\u679c \uff1d \uff0c\u4e14 \u662f\u7b2c\u56db\u8c61\u9650\u7684\u89d2\uff0c\u90a3\u4e48 \uff1d \uff1b
12. \u5df2\u77e5 \uff0c\u4e14 \uff0c\u5219 __________ \uff1b
13. \u5df2\u77e5 \u7684\u4e09\u4e2a\u5185\u89d2A\u3001B\u3001C\u6210\u7b49\u5dee\u6570\u5217\uff0c\u4e14 \u5219\u8fb9BC\u4e0a\u7684\u4e2d\u7ebfAD\u957f\u4e3a \uff1b
14. \u82e5 \u662f\u4ee55\u4e3a\u5468\u671f\u7684\u5947\u51fd\u6570\uff0c =4,\u4e14cos \uff0c\u5219 = .
\u4e09\u3001\u89e3\u7b54\u9898\uff08\u672c\u5927\u9898\u51716\u5c0f\u9898\uff0c\u517170\u5206\uff09
15\u3001\uff0812\u5206\uff09\u5df2\u77e5 \uff0c\u4e14 \u3001 \u662f\u65b9\u7a0b \u7684\u4e24\u4e2a\u6839\uff0c\u6c42COS\uff08 \uff09\u7684\u503c
16\uff0814\u5206\uff09 \u25b3ABC\u7684\u4e09\u4e2a\u5185\u89d2A\u3001B\u3001C\uff0c\u6c42\u5f53A\u4e3a\u4f55\u503c\u65f6\uff0c \u53d6\u5f97\u6700\u5927\u503c\uff0c\u5e76\u6c42\u51fa\u8fd9\u4e2a\u6700\u5927\u503c
17\uff0e\uff0814\u5206\uff09\u5df2\u77e5\u51fd\u6570 \uff08\u2160\uff09\u6c42 \u7684\u6700\u5c0f\u6b63\u5468\u671f\uff1b
\uff08\u2161\uff09\u6c42 \u7684\u6700\u5927\u503c\u548c\u6700\u5c0f\u503c\uff1b\uff08\u2162\uff09\u82e5 \uff0c\u6c42 \u7684\u503c.
18\uff0e\uff0812\u5206\uff09\u5982\u56fe\uff0c\u5f53\u7532\u8239\u4f4d\u4e8eA\u5904\u65f6\u83b7\u6089\uff0c\u5728\u5176\u6b63\u4e1c\u65b9\u5411\u76f8\u8ddd20\u6d77\u91cc\u7684B\u5904\u6709\u4e00\u8258
\u6e14\u8239\u9047\u9669\u7b49\u5f85\u8425\u6551\uff0e\u7532\u8239\u7acb\u5373\u524d\u5f80\u6551\u63f4\uff0c\u540c\u65f6\u628a\u6d88\u606f\u544a\u77e5\u5728\u7532\u8239\u7684\u5357\u504f\u897f30 \uff0c\u76f8\u8ddd10
\u6d77\u91ccC\u5904\u7684\u4e59\u8239\uff0c\u8bd5\u95ee\u4e59\u8239\u5e94\u671d\u5317\u504f\u4e1c\u591a\u5c11\u5ea6\u7684\u65b9\u5411\u6cbf\u76f4\u7ebf\u524d\u5f80B\u5904\u6551\u63f4\uff08\u89d2\u5ea6\u7cbe\u786e\u5230 \uff09\uff1f
19.\uff0814\u5206\uff09\uff0e\u5df2\u77e5 \u662f\u4e09\u89d2\u5f62 \u4e09\u5185\u89d2\uff0c\u5411\u91cf \uff0c\u4e14
\uff08\u2160\uff09\u6c42\u89d2 \uff1b\uff08\u2161\uff09\u82e5 \uff0c\u6c42
20\u3001\uff08 14\u5206\uff09\u5df2\u77e5b\u3001c\u662f\u5b9e\u6570\uff0c\u51fd\u6570f(x)= \u5bf9\u4efb\u610f\u03b1\u3001\u03b2 R\u6709\uff1a \u4e14
\uff081\uff09\u6c42f\uff081\uff09\u7684\u503c\uff1b\uff082\uff09\u8bc1\u660e\uff1aC \uff1b(3\uff09\u8bbe \u7684\u6700\u5927\u503c\u4e3a10\uff0c\u6c42f\uff08x\uff09\u3002
\u4e09\u89d2\u51fd\u6570\u6d4b\u8bd5\u5377\u53c2\u8003\u7b54\u6848
\u4e00\u3001\u9009\u62e9\u9898
DBBDB CCDDA
\u4e8c\u3001\u586b\u7a7a\u9898
11\u3001 12\u3001 13\u3001 14\u3001\u20144
\u4e09\u3001\u89e3\u7b54\u9898
15\u3001
16\u3001\u89e3: \u7531A+B+C=\u03c0, \u5f97B+C2 = \u03c02 \uff0dA2 , \u6240\u4ee5\u6709cosB+C2 =sinA2 .
cosA+2cosB+C2 =cosA+2sinA2 =1\uff0d2sin2A2 + 2sinA2
=\uff0d2(sinA2 \uff0d 12)2+ 32
\u5f53sinA2 = 12 , \u5373A=\u03c03 \u65f6, cosA+2cosB+C2\u53d6\u5f97\u6700\u5927\u503c\u4e3a32
17\uff0e\u89e3\uff1a
\uff08\u2160\uff09 \u7684\u6700\u5c0f\u6b63\u5468\u671f\u4e3a ;
\uff08\u2161\uff09 \u7684\u6700\u5927\u503c\u4e3a \u548c\u6700\u5c0f\u503c \uff1b
\uff08\u2162\uff09\u56e0\u4e3a \u5373 ,\u5373
18\u3001\u89e3 \u8fde\u63a5BC,\u7531\u4f59\u5f26\u5b9a\u7406\u5f97
BC2=202+102\uff0d2\u00d720\u00d710COS120\u00b0=700.
\u4e8e\u662f,BC=10 .
\u2235 , \u2234sin\u2220ACB= ,
\u2235\u2220ACB<90\u00b0 \u2234\u2220ACB=41\u00b0
\u2234\u4e59\u8239\u5e94\u671d\u5317\u504f\u4e1c71\u00b0\u65b9\u5411\u6cbf\u76f4\u7ebf\u524d\u5f80B\u5904\u6551\u63f4.
19\u3001\u89e3\uff1a\uff08\u2160\uff09\u2235 \u2234
\u5373
,
\u2235 \u2234 \u2234
\uff08\u2161\uff09\u7531\u9898\u77e5 \uff0c
\u6574\u7406\u5f97
\u2234 \u2234
\u2234 \u6216
\u800c \u4f7f \uff0c\u820d\u53bb \u2234
\u2234
20\u3001\u89e3\uff1a\uff081\uff09\u4ee4\u03b1= \uff0c\u5f97 \u4ee4\u03b2= \uff0c\u5f97 \u56e0\u6b64 \uff1b
\uff082\uff09\u8bc1\u660e\uff1a\u7531\u5df2\u77e5\uff0c\u5f53 \u65f6\uff0c
\u5f53 \u65f6\uff0c \u901a\u8fc7\u6570\u5f62\u7ed3\u5408\u7684\u65b9\u6cd5\u53ef\u5f97\uff1a \u5316\u7b80\u5f97c \uff1b
\uff083\uff09\u7531\u4e0a\u8ff0\u53ef\u77e5\uff0c[-1\uff0c1]\u662f \u7684\u51cf\u533a\u95f4\uff0c\u90a3\u4e48 \u53c8 \u8054\u7acb\u65b9\u7a0b\u7ec4\u53ef\u5f97 ,
\u6240\u4ee5
sin(-120 °）
=-sin(120 °)=-sin(180 °-60 °)=-sin60 °=-√3/2
2.
cos(-4π/3 )
=cos(4π/3)=cos(π+π/3)=-cos(π/3)=-1/2
3.
tan17π/6
=tan(3π-π/6)=tan(-π/6)=-tan(π/6)=-√3/3
4.
cos (-135°)=cos（135 °)=cos(180°-45°)=-cos45°=-√2/2
绛旓細1.sin(-120 掳锛=-sin(120 掳)=-sin(180 掳-60 掳)=-sin60 掳=-鈭3/2 2.cos(-4蟺/3 )=cos(4蟺/3)=cos(蟺+蟺/3)=-cos(蟺/3)=-1/2 3.tan17蟺/6 =tan(3蟺-蟺/6)=tan(-蟺/6)=-tan(蟺/6)=-鈭3/3 4.cos (-135掳)=cos锛135 掳)=cos(180掳-45掳)=-cos45...
绛旓細1銆乧os锛埾+a锛=-cosa=-1/2,cosa=1/2 a鍦ㄧ鍥涜薄闄 鎵浠ina<0 sin²a+cos²a=1 sina=-鈭3/2 sin(2蟺-a)=sin(-a)=-sina=鈭3/2 2銆乻in(2蟺-a)=sin(-a)=-sina 5cos锛2蟺-a锛/2cos(蟺+a)=5cos(-a)/2(-cosa)=5cosa/(-2cosa)=-5/2 sin(-a)=-sina...
绛旓細1. cos2x=1-2*(sinx)^2 鏁 f(sinx)=3-cos2x=2+2*(sinx)^2 鍗 f(x)=2+2*x^2 鎵浠 f(cosx)=2+2*(cosx)^2=2+1+[2*(cosx)^2-1]=3+cos2x 寰桟 2. sin(7蟺/6 +a)=sin(2蟺/3 +a+蟺/2)=cos(2蟺/3 +a) = -1/4 锛 cos(5蟺/6 -a)=cos(-...
绛旓細=sin(蟺+x)=-sinx 瑙ｆ硶鍒嗘瀽锛氬埄鐢ㄤ笁瑙掑嚱鏁扮殑璇卞鍏紡锛屽氨鍙互寰堝揩寰楀嚭缁撴灉銆涓夎鍑芥暟璇卞鍏紡濡備笅锛1銆佺涓缁 sin (伪+k路360掳)=sin伪锛坘鈭圸锛夛紝cos(伪+k路360掳)=cos伪锛坘鈭圸锛夛紝tan (伪+k路360掳)=tan伪锛坘鈭圸锛夛紝cot锛埼+k路360掳锛=cot伪 锛坘鈭圸锛夛紱sec锛埼+k路360掳锛=s...
绛旓細鍗-2tana+3sinb+5=0 tana-6sinb-1=0 鎵浠inb=1/3,tana=3 sina/cosa=tana=3 cosa=1/3*sina cos²a=1/9*sin²a 鍥犱负si²a+cos²a=1 鎵浠in²a=9/10 a鏄攼瑙掑垯sina>0 sina=3鈭10/10
绛旓細宸茬煡鏂圭▼sinx+cosx=k鍦0鈮鈮は涓婃湁涓よВ锛屾眰k鐨勫彇鍊艰寖鍥 銆愯В鏋愩戝師鏂圭▼sinx+cosx=k sin锛坸+ 锛=k锛屽湪鍚屼竴鍧愭爣绯诲唴浣鍑芥暟y1= sin锛坸+ 锛変笌y2=k鐨勫浘璞.瀵逛簬y= sin锛坸+ 锛夛紝浠=0锛屽緱y=1.鈭村綋k鈭堛1锛屻曟椂锛岃瀵熺煡涓ゆ洸绾垮湪銆0锛屜銆曚笂鏈変袱浜ょ偣锛屾柟绋嬫湁涓よВ.銆愮偣璇勩戞湰棰樻槸閫氳繃...
绛旓細A+B=180-C cosx=-cos(180-x)鎵浠閿 鍥犱负sinx=sin(180-x)鎵浠姝ｇ‘ tanx=-tan(180-x)鎵浠閿 sinx=cos(90-x)鍒(A+B)/2=90-C/2 鎵浠閿 鎵浠ラ塀
绛旓細cos(x+螤锛=-cosx 杩愮敤涓夎鍑芥暟鐨勮瀵煎叕寮忓彲浠ヨВ棰橈紝璇卞鍏紡鐨鍙ｈ瘈鏄滃鍙樺伓涓嶅彉锛岀鍙风湅璞￠檺鈥濓紝鍗崇浉鍔犵殑鍊煎鏋滄槸螤/2鐨勫鏁板嶏紝灏辫鎶妔in\cos浜掔浉鍙樺寲锛岀鍙风湅璞￠檺鎸噚+螤鐨勮薄闄愬喅瀹氫簡鏈鍚庣粨鏋滅殑姝ｈ礋銆
绛旓細瀵逛簬涓鑸儏鍐礳os(伪+k蟺/2)鐨勫垽鏂紝鎶娢辩湅鍋氫竴涓攼瑙掑幓鍒ゆ柇锛屽叿浣撳涓嬶細鈥濆鍙樺伓涓嶅彉鈥滄槸鎸囄+k蟺/2閲岄潰鐨刱鏄鏁拌繕鏄伓鏁帮紝鏄鏁扮殑璇濆氨瑕佸彉鎴愭寮﹀嚱鏁帮紝鍚﹀垯杩樻槸浣欏鸡鍑芥暟鐨褰㈠紡锛氳繖閲屾樉鐒秌=-1锛屼负濂囨暟锛屾晠搴旇鍙樻垚(+/-)sin伪褰㈠紡,绗﹀彿鏈夊緟纭畾锛涒滅鍙风湅璞￠檺鈥濇槸鍦ㄦ妸伪瑙嗕綔閿愯鐨勬椂鍊欏垽鏂...
绛旓細棣栧厛cos伪=2/3锛屾眰寰梥in伪=姝ｈ礋鏍瑰彿5/3锛岀敱伪鐨勫煙寰梥in伪=璐熶笁鍒嗕箣鏍瑰彿浜旓紱姹傚緱tan伪璐熶簩鍒嗕箣鏍瑰彿浜旓紝tan锛-伪-蟺锛=姝ｄ簩鍒嗕箣鏍瑰彿浜旓紝sin锛2蟺+伪锛=璐熸牴鍙蜂笁鍒嗕箣鏍瑰彿浜旓紝cos锛埼憋級=cos锛-伪锛夛紝tan锛埾+伪锛=tan伪銆傜患涓婂彲浠ユ眰鍑轰綘瑕佺殑鍊 ...
