[分享] 三角函数及其变换

无名英雄 发表于 2006-5-15 21:11:00

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<TD align=middle width=673>三角函数及其变换</TD></TR></TBODY></TABLE></CENTER>
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<TD width=40>定义:</TD>
<TD width=630 colSpan=3>   设a是一个任意大小的角, 角α的终边上任意一点P的坐标是（x,y）, 它与原点的距离是r（r>0）, 那么角α的六个三角函数定义如下：
<P language=Javascript1.2 id=fpAnimflyTopLeftFP1 style="LEFT: 0px; VISIBILITY: visible; MARGIN: 3px 0px 0px; WORD-SPACING: 0px; TEXT-INDENT: 0px; LINE-HEIGHT: 100%; POSITION: relative! important; TOP: 0px" endTop="0" endLeft="0" initTop="-161" initLeft="-310" startL="210" dynamicanimation="fpAnimflyTopLeftFP1">  正弦(sine)      : sinα=y/r
<P language=Javascript1.2 id=fpAnimflyTopLeftFP2 style="LEFT: 0px; VISIBILITY: visible; MARGIN: 3px 0px 0px; WORD-SPACING: 0px; TEXT-INDENT: 0px; LINE-HEIGHT: 100%; POSITION: relative! important; TOP: 0px" endTop="0" endLeft="0" initTop="-180" initLeft="-310" startL="210" dynamicanimation="fpAnimflyTopLeftFP2">  余弦(cosine)    : cosα=x/r
<P language=Javascript1.2 id=fpAnimflyTopLeftFP3 style="LEFT: 0px; VISIBILITY: visible; MARGIN: 3px 0px 0px; WORD-SPACING: 0px; TEXT-INDENT: 0px; LINE-HEIGHT: 100%; POSITION: relative! important; TOP: 0px" endTop="0" endLeft="0" initTop="-199" initLeft="-310" startL="210" dynamicanimation="fpAnimflyTopLeftFP3">  正切(tangent)   : tanα=y/x
<P language=Javascript1.2 id=fpAnimflyTopLeftFP4 style="LEFT: 0px; VISIBILITY: visible; MARGIN: 3px 0px 0px; WORD-SPACING: 0px; TEXT-INDENT: 0px; LINE-HEIGHT: 100%; POSITION: relative! important; TOP: 0px" endTop="0" endLeft="0" initTop="-218" initLeft="-310" startL="210" dynamicanimation="fpAnimflyTopLeftFP4">  余切(cotangent) : cotα=x/y
<P language=Javascript1.2 id=fpAnimflyTopLeftFP5 style="LEFT: 0px; VISIBILITY: visible; MARGIN: 3px 0px 0px; WORD-SPACING: 0px; TEXT-INDENT: 0px; LINE-HEIGHT: 100%; POSITION: relative! important; TOP: 0px" endTop="0" endLeft="0" initTop="-237" initLeft="-310" startL="210" dynamicanimation="fpAnimflyTopLeftFP5">  正割(secant)    : secα=r/x
<P language=Javascript1.2 id=fpAnimflyTopLeftFP6 style="LEFT: 0px; VISIBILITY: visible; MARGIN: 3px 0px 0px; WORD-SPACING: 0px; TEXT-INDENT: 0px; LINE-HEIGHT: 100%; POSITION: relative! important; TOP: 0px" endTop="0" endLeft="0" initTop="-256" initLeft="-310" startL="210" dynamicanimation="fpAnimflyTopLeftFP6">  余割(cosecant)  : cscα=r/y
　</TD></TR>
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<TD width=676 colSpan=4>三角函数式的变换</TD></TR>
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<TD width=40>
倒数</TD>
<TD width=206>
sinα*cscα=1</TD>
<TD width=220>
cosα*secα=1</TD>
<TD width=189>
tanα*cotα=1</TD></TR>
<TR>
<TD width=40>
商数</TD>
<TD width=206>
tanα=sinα/cosα</TD>
<TD width=220>
cotα=cosα/sinα</TD>
<TD width=189>
　</TD></TR>
<TR>
<TD width=40>
平方和</TD>
<TD width=206>
sin2α+cos2α=1</TD>
<TD width=220>
1+tan2α=sec2α</TD>
<TD width=189>
1+cot2α=csc2α</TD></TR>
<TR>
<TD width=40>
两角和</TD>
<TD width=206>
sin(α±β)=sinαcosβ+cosαsinβ</TD>
<TD width=220>
cos(α±β)=cosαcosβ-+sinαsinβ</TD>
<TD width=189>
tan(α±β)=(tanα±tanβ)/(1-+tanαtanβ)</TD></TR>
<TR>
<TD width=40>
倍角</TD>
<TD width=206>
sin2α=2sinαcosα</TD>
<TD width=220>
cos2α=cos2α-sin2α=2cos2α-1
     =1-2sin2α</TD>
<TD width=189>
tan2α=2tanα/(1-tan2α)</TD></TR>
<TR>
<TD width=40>
半角</TD>
<TD width=206>
sin(α/2)=[(1-cosα)/2]^0.5</TD>
<TD width=220>
cos(α/2)=[(1+cosα)/2]^0.5</TD>
<TD width=189>
tan(α/2)
=[(1-cosα)/(1+cosα)]^0.5</TD></TR>
<TR>
<TD width=40>
和差
化积</TD>
<TD width=206>
sinαcosβ
=/2</TD>
<TD width=220>
cosαsinβ
=/2</TD>
<TD width=189 rowSpan=4>
　 
　       </TD></TR>
<TR>
<TD width=40>
和差
化积</TD>
<TD width=206>
sinαsinβ
=/2</TD>
<TD width=220>
cosαcosβ
=-/2</TD></TR>
<TR>
<TD width=40>
积化
和差</TD>
<TD width=206>
sinα+sinβ
=2sin[(α+β)/2]cos[(α-β)/2]</TD>
<TD width=220>
sinα-sinβ
=2cos[(α+β)/2]sin[(α-β)/2]</TD></TR>
<TR>
<TD width=40>
积化
和差</TD>
<TD width=206>
cosα+cosβ
=2cos[(α+β)/2]cos[(α-β)/2]</TD>
<TD width=220>
cosα-cosβ
=-2sin[(α+β)/2]sin[(α-β)/2]</TD></TR></TBODY></TABLE></CENTER></DIV>

308247504 发表于 2006-6-13 19:59:00

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[分享] 三角函数及其变换