| 作曲 : 石伟 | |
| 作词 : 石伟 | |
| 歌曲歌词请见《洛天依 - 三角函数歌诀》 | |
| 三角函数公式小结： | |
| 1、象限角三角函数正负 | |
| 一全正,二正弦,三正切,四余弦 | |
| 2、三角函数诱导公式 | |
| (1)sin(a+2兀k)=sina | |
| (cos,tan也相同,k属于Z) | |
| (2)sin(兀+a)=-sina | |
| cos(兀+a)=-cosa | |
| tan(兀+a)=tana | |
| (3)sin(-a)=-sina | |
| cos(-a)=cosa | |
| tan(-a)=-tana | |
| (4)sin(兀-a)=sina | |
| cos(兀-a)=-cosa | |
| tan(兀-a)=-tana | |
| (5)sin(兀/2-a)=cosa | |
| cos(兀/2-a)=sina | |
| tan(兀/2-a)=cota | |
| (6)sin(兀/2+a)=cosa | |
| cos(兀/2+a)=-sina | |
| tan(兀/2+a)=-cota | |
| 奇变偶不变,符号看象限 | |
| 3、同三角函数基本关系公式 | |
| (1)sin^2(a)+cos^2(a)=1 | |
| (2)sina/cosa=tana | |
| (3)sina=cosatana | |
| (4)(sina+-cosa)^2=1+-2sinacosa | |
| (5)tan^2(a)+1=1/(cosa^2) | |
| (6)cota=1/tana | |
| 4、和角公式与差角公式 | |
| (1)cos(a+b)=cosacosb-sinasinb | |
| cos(a-b)=cosacosb+sinasinb | |
| (2)sin(a+b)=sinacosb+cosasinb | |
| sin(a-b)=sinacosb-cosasinb | |
| (3)tan(a+b)=(tana+tanb)/(1-tanatanb) | |
| tan(a-b)=(tana-tanb)/(1+tanatanb) | |
| 余余正正号相反, | |
| 正余余正号相同, | |
| 正切和除一积差。 | |
| 5、倍角公式与半角公式 | |
| (1)二倍 | |
| sin2a=2sinacosa | |
| cos2a=cosa^2-sina^2 | |
| =2cosa^2-1=1-2sina^2 | |
| tana=2tana/(1-tana^2) | |
| 正倍二正余,余倍平方差, | |
| 切倍二正切,除一平方差。 | |
| (2)三倍 | |
| sin3a=3sina-4sina^2 | |
| cos3a=4cosa^2-3cosa | |
| tan3a=-tana^2tan(兀/2-a) | |
| 6、和差化积 | |
| sina+sinb=2sin［(a+b)/2］cos［(a-b)/2］ | |
| cosa+cosb=2cos［(a+b)/2］cos［(a-b)/2］ | |
| sina-sinb=2cos［(a+b)/2］sin［(a-b)/2］ | |
| cosa-cosb=-2sin［(a+b)/2］sin［(a-b)/2］ | |
| 7、积化和差 | |
| sinacosb=［sin(a+b)+sin(a-b)］/2 | |
| cosasinb=［sin(a+b)-sin(a-b)］/2 | |
| cosacosb=［cos(a+b)+cos(a-b)］/2 | |
| sinasinb=-［cos(a+b)-cos(a-b)］/2 | |
| 8、合一变形 | |
| Asinwx+Bcoswx=(A^2+B^2)^-2sin(wx+c) | |
| 9、半角公式 | |
| (sina/2)^2=(1-cosa)/2 | |
| (cosa/2)^2=(1+cosa)/2 | |
| (tana/2)^2=(1-cosa)/(1+cosa) | |
| 10、万能公式 | |
| 若tana/2=t | |
| 则sina=2t/(1+t^2) | |
| cosa=(1-t^2)/(1+t^2) | |
| tana=2t/(1-t^2) |
| zuo qu : shi wei | |
| zuo ci : shi wei | |
| ge qu ge ci qing jian luo tian yi san jiao han shu ge jue | |
| san jiao han shu gong shi xiao jie: | |
| 1 xiang xian jiao san jiao han shu zheng fu | |
| yi quan zheng, er zheng xian, san zheng qie, si yu xian | |
| 2 san jiao han shu you dao gong shi | |
| 1 sin a 2 wu k sina | |
| cos, tan ye xiang tong, k shu yu Z | |
| 2 sin wu a sina | |
| cos wu a cosa | |
| tan wu a tana | |
| 3 sin a sina | |
| cos a cosa | |
| tan a tana | |
| 4 sin wu a sina | |
| cos wu a cosa | |
| tan wu a tana | |
| 5 sin wu 2a cosa | |
| cos wu 2a sina | |
| tan wu 2a cota | |
| 6 sin wu 2 a cosa | |
| cos wu 2 a sina | |
| tan wu 2 a cota | |
| qi bian ou bu bian, fu hao kan xiang xian | |
| 3 tong san jiao han shu ji ben guan xi gong shi | |
| 1 sin 2 a cos 2 a 1 | |
| 2 sina cosa tana | |
| 3 sina cosatana | |
| 4 sina cosa 2 1 2sinacosa | |
| 5 tan 2 a 1 1 cosa 2 | |
| 6 cota 1 tana | |
| 4 he jiao gong shi yu cha jiao gong shi | |
| 1 cos a b cosacosbsinasinb | |
| cos ab cosacosb sinasinb | |
| 2 sin a b sinacosb cosasinb | |
| sin ab sinacosbcosasinb | |
| 3 tan a b tana tanb 1tanatanb | |
| tan ab tanatanb 1 tanatanb | |
| yu yu zheng zheng hao xiang fan, | |
| zheng yu yu zheng hao xiang tong, | |
| zheng qie he chu yi ji cha. | |
| 5 bei jiao gong shi yu ban jiao gong shi | |
| 1 er bei | |
| sin2a 2sinacosa | |
| cos2a cosa 2sina 2 | |
| 2cosa 21 12sina 2 | |
| tana 2tana 1tana 2 | |
| zheng bei er zheng yu, yu bei ping fang cha, | |
| qie bei er zheng qie, chu yi ping fang cha. | |
| 2 san bei | |
| sin3a 3sina4sina 2 | |
| cos3a 4cosa 23cosa | |
| tan3a tana 2tan wu 2a | |
| 6 he cha hua ji | |
| sina sinb 2sin a b 2 cos ab 2 | |
| cosa cosb 2cos a b 2 cos ab 2 | |
| sinasinb 2cos a b 2 sin ab 2 | |
| cosacosb 2sin a b 2 sin ab 2 | |
| 7 ji hua he cha | |
| sinacosb sin a b sin ab 2 | |
| cosasinb sin a b sin ab 2 | |
| cosacosb cos a b cos ab 2 | |
| sinasinb cos a b cos ab 2 | |
| 8 he yi bian xing | |
| Asinwx Bcoswx A 2 B 2 2sin wx c | |
| 9 ban jiao gong shi | |
| sina 2 2 1cosa 2 | |
| cosa 2 2 1 cosa 2 | |
| tana 2 2 1cosa 1 cosa | |
| 10 wan neng gong shi | |
| ruo tana 2 t | |
| ze sina 2t 1 t 2 | |
| cosa 1t 2 1 t 2 | |
| tana 2t 1t 2 |
| zuò qǔ : shí wěi | |
| zuò cí : shí wěi | |
| gē qǔ gē cí qǐng jiàn luò tiān yī sān jiǎo hán shù gē jué | |
| sān jiǎo hán shù gōng shì xiǎo jié: | |
| 1 xiàng xiàn jiǎo sān jiǎo hán shù zhèng fù | |
| yī quán zhèng, èr zhèng xián, sān zhèng qiē, sì yú xián | |
| 2 sān jiǎo hán shù yòu dǎo gōng shì | |
| 1 sin a 2 wù k sina | |
| cos, tan yě xiāng tóng, k shǔ yú Z | |
| 2 sin wù a sina | |
| cos wù a cosa | |
| tan wù a tana | |
| 3 sin a sina | |
| cos a cosa | |
| tan a tana | |
| 4 sin wù a sina | |
| cos wù a cosa | |
| tan wù a tana | |
| 5 sin wù 2a cosa | |
| cos wù 2a sina | |
| tan wù 2a cota | |
| 6 sin wù 2 a cosa | |
| cos wù 2 a sina | |
| tan wù 2 a cota | |
| qí biàn ǒu bù biàn, fú hào kàn xiàng xiàn | |
| 3 tóng sān jiǎo hán shù jī běn guān xì gōng shì | |
| 1 sin 2 a cos 2 a 1 | |
| 2 sina cosa tana | |
| 3 sina cosatana | |
| 4 sina cosa 2 1 2sinacosa | |
| 5 tan 2 a 1 1 cosa 2 | |
| 6 cota 1 tana | |
| 4 hé jiǎo gōng shì yǔ chà jiǎo gōng shì | |
| 1 cos a b cosacosbsinasinb | |
| cos ab cosacosb sinasinb | |
| 2 sin a b sinacosb cosasinb | |
| sin ab sinacosbcosasinb | |
| 3 tan a b tana tanb 1tanatanb | |
| tan ab tanatanb 1 tanatanb | |
| yú yú zhèng zhèng hào xiāng fǎn, | |
| zhèng yú yú zhèng hào xiāng tóng, | |
| zhèng qiē hé chú yī jī chà. | |
| 5 bèi jiǎo gōng shì yǔ bàn jiǎo gōng shì | |
| 1 èr bèi | |
| sin2a 2sinacosa | |
| cos2a cosa 2sina 2 | |
| 2cosa 21 12sina 2 | |
| tana 2tana 1tana 2 | |
| zhèng bèi èr zhèng yú, yú bèi píng fāng chà, | |
| qiè bèi èr zhèng qiē, chú yī píng fāng chà. | |
| 2 sān bèi | |
| sin3a 3sina4sina 2 | |
| cos3a 4cosa 23cosa | |
| tan3a tana 2tan wù 2a | |
| 6 hé chà huà jī | |
| sina sinb 2sin a b 2 cos ab 2 | |
| cosa cosb 2cos a b 2 cos ab 2 | |
| sinasinb 2cos a b 2 sin ab 2 | |
| cosacosb 2sin a b 2 sin ab 2 | |
| 7 jī huà hé chà | |
| sinacosb sin a b sin ab 2 | |
| cosasinb sin a b sin ab 2 | |
| cosacosb cos a b cos ab 2 | |
| sinasinb cos a b cos ab 2 | |
| 8 hé yī biàn xíng | |
| Asinwx Bcoswx A 2 B 2 2sin wx c | |
| 9 bàn jiǎo gōng shì | |
| sina 2 2 1cosa 2 | |
| cosa 2 2 1 cosa 2 | |
| tana 2 2 1cosa 1 cosa | |
| 10 wàn néng gōng shì | |
| ruò tana 2 t | |
| zé sina 2t 1 t 2 | |
| cosa 1t 2 1 t 2 | |
| tana 2t 1t 2 |
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