sin10怎么算（不用计算器）

\u4e09\u89d2\u51fd\u6570\u4e0d\u7528\u8ba1\u7b97\u5668\u5982\u4f55\u7b97?

\u73b0\u5728\u6570\u5b66\u8bfe\u672c\u53ea\u6d89\u53ca\u4e00\u4e9b\u7279\u5b9a\u53ef\u7b97\u7684\u89d2\uff0c\u598215\uff0c30\uff0c45\uff0c60\uff0c75\uff0c90\u5ea6\u89d2\u3002\u7531\u4e09\u89d2\u51fd\u6570\u516c\u5f0f\u53ef\u4ee5\u8ba1\u7b97\u51fa\u51c6\u786e\u503c\u3002\u4e5f\u662f\u6bd4\u8f83\u5e38\u89c1\u7684\u3002
\u59821.5\uff0c23.3\uff0c52.5\u7b49\u975e\u7279\u6b8a\u89d2\uff0c\u7528\u7b14\u7b97\u8ba1\u7b97\u7684\u65b9\u6cd5\u5f88\u96be\u89e3\uff0c\u8bd5\u9898\u4e2d\u4e5f\u5f88\u5c11\u51fa\u73b0\u3002

\u4ee5\u4e0b\u662f\u4e00\u4e9b\u5e38\u89c1\u7684\u4e09\u89d2\u51fd\u6570\u516c\u5f0f\uff1a
1.\u8bf1\u5bfc\u516c\u5f0f

sin(-a)=-sin(a)

cos(-a)=cos(a)

sin(\u03c02-a)=cos(a)

cos(\u03c02-a)=sin(a)

sin(\u03c02+a)=cos(a)

cos(\u03c02+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)�6�1sin(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�6�6[cos(a+b)-cos(a-b)]

cos(a)cos(b)=12�6�6[cos(a+b)+cos(a-b)]

sin(a)cos(b)=12�6�6[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�6�6sin(a)+b�6�6cos(a)=a2+b2sin(a+c) \u5176\u4e2d tan(c)=ba

a�6�6sin(a)-b�6�6cos(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




\u5176\u4ed6\u975e\u91cd\u70b9

csc(a)=1sin(a)

sec(a)=1cos(a)

\u53cd\u590d\u505a\uff0c\u98a0\u5012\u505a
\u52a0\u6570\u52a0\u53e6\u4e00\u4e2a\u52a0\u6570=\u548c\uff0c\u52a0\u6570=\u548c-\u53e6\u4e00\u4e2a\u52a0\u6570\uff0c\u548c=\u52a0\u6570+\u53e6\u4e00\u4e2a\u52a0\u6570
\u88ab\u51cf\u6570-\u51cf\u6570=\u5dee\uff0c\u51cf\u6570=\u88ab\u51cf\u6570-\u5dee\uff0c\u88ab\u51cf\u6570=\u51cf\u6570+\u5dee\uff0c\u5dee=\u88ab\u51cf\u6570-\u51cf\u6570\uff0c\u88ab\u51cf\u6570-\u5dee=\u51cf\u6570
AxB=C\uff0cA=C\u00f7B\uff0cB=C\u00f7A\uff0cC=AxB \u7528\u8bed\u8a00\u63cf\u8ff0
A\u00f7B=C\uff0cA=BxC\uff0cB=A\u00f7C\uff0cC=A\u00f7B \u7528\u8bed\u8a00\u63cf\u8ff0

用泰勒公式啊！ 泰勒公式是专门用来求某一复杂函数的近似值的.在泰勒公式中sinx=x-x^3/3!+x^5/5!-x^7/7!+x^9/9!......依次类推,可能计算比较麻烦,但这是目前解决这类问题的好方法,不妨试试.

没有确切算法的,用tan10*cos10吧,结果必定大于零

sin10=sin(3*pi+0.18*pi)=-sin(0.18*pi)=-sin(32度)约=-0.5

sin10鎬庝箞绠(涓嶇敤璁＄畻鍣)
绛旓細鐢ㄦ嘲鍕掑叕寮忓晩锛 娉板嫆鍏紡鏄笓闂ㄧ敤鏉ユ眰鏌愪竴澶嶆潅鍑芥暟鐨勮繎浼煎肩殑.鍦ㄦ嘲鍕掑叕寮忎腑sinx=x-x^3/3!+x^5/5!-x^7/7!+x^9/9!...渚濇绫绘帹,鍙兘璁＄畻姣旇緝楹荤儲,浣嗚繖鏄洰鍓嶈В鍐宠繖绫婚棶棰樼殑濂芥柟娉,涓嶅Θ璇曡瘯.

姹sin10sin40sin70鐨勫(瑙ｇ瓟杩囩▼;涓嶈璁＄畻鍣鐨)
绛旓細sin10sin40sin70=2sin10cos10sin40sin(90-20锛/2cos10 =sin20cos20sin40/2cos10 =sin40sin40/4sin80 =sin40sin40/2sin40cos40=0.5tan40(濡傛灉棰樼洰娌＄瑪璇紝灏卞彧鑳借繖鏍蜂簡)

涓嶄娇鐢ㄨ绠楀櫒鎬庝箞璁＄畻sin10掳鐨勫?
绛旓細sin(x)=x-x^3/(3!)+x^5/(5!)-x^7/(7!)+...=x-x^3/6+x^5/120-x^7/5040+...锛1锛夋澶剎鏄姬搴﹁屼笉鏄搴.鑻ョ敤寮у害,sin(10)灏卞簲琛ㄨ揪鎴恠in(蟺/18),鍗硏=蟺/18.灏唜=蟺/18浠ｅ叆寮忥紙1锛,骞剁敤锛1锛夊紡鐨勫墠4椤瑰仛杩戜技璁＄畻,鍗冲緱锛歴in(蟺/18)鈮0.17364817766652.鑻鐢ㄨ绠楀櫒...

sin10掳涓嶇敤璁＄畻鏈瑕鎬庝箞姹?
绛旓細=x-x^3/6+x^5/120-x^7/5040+... 锛1锛夋澶剎鏄姬搴﹁屼笉鏄搴︺傝嫢鐢ㄥ姬搴︼紝sin(10)灏卞簲琛ㄨ揪鎴恠in(蟺/18)锛屽嵆x=蟺/18銆傚皢x=蟺/18浠ｅ叆寮忥紙1锛夛紝骞剁敤锛1锛夊紡鐨勫墠4椤瑰仛杩戜技璁＄畻锛屽嵆寰楋細sin(蟺/18)鈮0.17364817766652銆傝嫢鐢ㄨ绠楀櫒绠楋紝鍙緱sin(10)=0.17364817766693 涓よ呬粎鍦ㄥ皬鏁扮偣...

閿愯涓夎鍑芥暟 姣旇緝澶у皬涓嶇敤璁＄畻鍣姣旇緝sin10 sin 50 cos70 鐨勫ぇ灏...
绛旓細鎴戞潵鍋氬惂.cos70=sin20,y=sinX鍑芥暟鍦紙0,90锛変箣闂存槸涓ユ牸鐨勫崟璋冮掑鍑芥暟,鎵浠 sin10

sin10濡備綍鐭ラ亾鏄杩樻槸璐(涓嶇敤璁＄畻鍣)
绛旓細涓鸿礋銆10=3蟺+伪锛屽湪绗笁璞￠檺锛屾寮﹀嚱鏁颁负璐熴

宸茬煡瑙掑害/寮у害姹傛寮(绂佺敤璁＄畻鍣) PS.涓嶇煡閬撳杈归偦杈规枩杈逛笖涓嶆槸鐗规畩瑙...
绛旓細鑰宻in7掳=sin(3掳+4掳),鍒╃敤鍜岃鍏紡姹.杩欐牱涓鏉1掳鍒10掳鐨勬寮﹂兘姹傚嚭鏉ヤ簡,杩涜屾牴鎹拰瑙掑叕寮,鍙互姹11掳,12掳,...浠讳綍鏁存暟瑙掑害鐨勬寮.涓嶈繃杩欐牱鍋氱殑鎰忎箟涓嶅ぇ.鍥犱负铏界劧鐢ㄥ叕寮忔眰鍑烘潵鐨勬槸绮剧‘鍊,浣嗘牴鍙峰甫寰楀お澶,鏍瑰彿鐨勮绠楅噺涔熸槸鍗佸垎澶х殑.鍦涓嶇敤璁＄畻鍣鐨勬儏鍐典笅,寰堝洶闅.鎵浠ュ鏂艰繖绉嶈绠楀緢澶氱殑...

sin10鎬庝箞绠
绛旓細sin10绛変簬0.1736銆1銆侀鍏堬紝寮у害=(蟺/180)x瑙掑害銆2銆佸叾娆★紝sin10=sin(10x蟺/180)锛屽叾涓紝蟺鏄渾鍛ㄧ巼锛岀瓑浜3.14159銆3銆佹渶鍚庯紝閫氳繃璁＄畻鍣鐨勪笁瑙掑嚱鏁板嚱鏁帮紝鍙互寰楀嚭sin10绛変簬0.1736銆

璇烽棶sin10搴﹁兘鏍瑰彿璁＄畻鍑烘潵鍚?
绛旓細杩涗竴姝ュ湴锛屾垜浠彲浠ュ埄鐢ㄦ寮20搴︾殑鍊硷紝鍥犱负 \( \sin20掳 \) 鍙互閫氳繃鏌ヨ〃鎴栬璁＄畻鍣寰楀嚭锛屽畠绛変簬澶х害 \( 0.3420201433 \) (鍥涜垗浜斿叆鍒板皬鏁扮偣鍚8浣)銆傝繖鏍凤紝鎴戜滑寰楀埌鐨勬柟绋嬫槸 \( x^2 = \frac{1}{2} \times 0.3420201433 \)銆備负浜嗚В鍑 \( x \)锛屽嵆姝ｅ鸡10搴︾殑鍊硷紝鎴戜滑闇瑕佸杩欎釜鏂圭▼...

sin10搴︾瓑浜庡灏?
绛旓細棰濓紝浣犵殑璁＄畻鏈涓婂簲璇ユ湁璁＄畻鍣鍚э紝涓嶄細鐢紵鎹㈡垚绉戝璁＄畻鍣紝灏卞彲浠ヤ簡 sin10掳=0.1736481776669

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