公式备查
同角三角函数基本恒等式
sin?cos? cot?? cos?sin?111 sec?? cot?? csc??sin?cos?tan?tan??sin2??cos2??1 sec2??tan2??1 csc2??cot2??1
诱导公式 (奇变偶不变,符号看象限)
sin(??)??sin?sin(???)?sin?sin(???)??sin?cos(??)?cos? cos(???)??cos? cos(???)??cos? tan(??)??tan?tan(???)?tan?tan(???)??tan?sin(2k???)?sin?tan(2k???)?tan?sin(sin(2???)?—sin?cos(2k???)?cos? cos(2???)?cos?tan(2???)??tan?sin(
3?3???)??cos?sin(??)??cos?2222??3?3?cos(??)?sin? cos(??)??sin? cos(??)??sin? cos(??)?sin?
2222??3?3?tan(??)?cot?tan(??)??cot?tan(??)?cot?tan(??)??cot?2222??)?cos???)?cos?sin(??和(差)角公式
sin(???)?sin?cos??cos?sin? cos(???)?cos?cos??sin?sin? sin(???)?sin?cos??cos?sin? cos(???)?cos?cos??sin?sin? tan(???)?tan??tan?tan??tan? tan(???)?
1?tan??tan?1?tan??tan?倍角公式 sin2??2sin?cos? tan2??2tan?
1?tan2?cos2??cos2??sin2??1?2sin2??2cos2??1
半角公式 sintan?2??1?cos??1?cos? cos?? 2221?cos?sin?1?cos??? (符号看象限)
1?cos?1?cos?sin??2??1?cos2?1?cos2? cos2?? 221?cos2? tan2??
1?cos2?降幂扩角公式 sin2??三倍角公式 sin3??3sin??4sin3? cos3??4cos3??3cos?
和差化积公式
sin??sin??2sin???2222???????????? cos??cos???2sincos??cos??2coscossin2222cos??? sin??sin??2cos???sin???
积化和差公式
11sin?cos??[sin(???)?sin(???)] cos?sin??[sin(???)?sin(???)]
2211cos?cos??[cos(???)?cos(???)] sin?sin???[cos(???)?cos(???)]
22其他常用公式
(a?b)2?a2?2ab?b2 logaM?logaN?logaMN a2?b2?(a?b)(a?b) logaM?logaN?loga(a?b)3?a3?3a2b?3ab2?b3 logaMn?nlogaM a3?b3?(a?b)(a2?b2?ab) alogaN?N
M N
关于反三角函数
1、反正弦函数 y?arcsinx x?[?1,1] 是正弦函数y?sinx x?[?,] 的反函数
22??反余弦函数 y?arccosx x?[?1,1] 是余弦函数y?cosx x?[0,?] 的反函数 反正切函数 y?arctanx x?(??,??) 是正切函数y?sinx x?(?,) 的反函数
22??
2、arcsin(??)??arcsin? arctan(??)??arctan?
??)???arccos? arccot(??)???arccot? arccos(3、sinsin?6??33?11?? arcsin? sin? arcsin3223226?2?1 arcsin1??2 sin??0 arcsin0??
cos?6?33??11? arccos? cos? arccos? 2263223cos?2?0 arccos0??2 cos???1 arccos(?1)??
tan?6?3?3??? tan?3 arctan3? arctan36333tan?4?1 arctan1??4 tan0?0 arctan0?0