函數
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三角、對數與指數
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範例：雙曲線與反雙曲線函數
範例：雙曲線與反雙曲線函數
顯示將雙曲線函數的計算結果傳遞給對應的反雙曲線函數，會傳回原始輸入引數。
1.
定義輸入引數
z
，並以符號方式與數值方式進行計算：
<region id="ID0EDS4KB" actualWidth="74.393333333333331" actualHeight="47.2" top="19.200000000000003" left="0" xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="14" xml:lang="zh_TW"> <define xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50"> <id labels="VARIABLE" xml:space="preserve" xml:lang="zh_TW">z</id> <apply xml:lang="zh_TW"> <plus xml:lang="zh_TW" /> <apply xml:lang="zh_TW"> <div xml:lang="zh_TW" /> <id labels="CONSTANT" xml:space="preserve" xml:lang="zh_TW">π</id> <real xml:lang="zh_TW">2</real> </apply> <imag symbol="i" xml:lang="zh_TW">1</imag> </apply> </define> </math> </region>
<region id="ID0EVS4KB" actualWidth="167.14999999999998" actualHeight="51.158666666666669" top="76.800000000000011" left="0" xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="15" xml:lang="zh_TW"> <eval xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50"> <symEval xml:lang="zh_TW"> <id labels="VARIABLE" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">z</id> <command xml:lang="zh_TW"> <placeholder xml:lang="zh_TW" /> </command> <symResult xml:lang="zh_TW"> <apply xml:lang="zh_TW"> <plus xml:lang="zh_TW" /> <apply xml:lang="zh_TW"> <div xml:lang="zh_TW" /> <id labels="CONSTANT" xml:space="preserve" xml:lang="zh_TW">π</id> <real xml:lang="zh_TW">2</real> </apply> <imag symbol="i" xml:lang="zh_TW">1</imag> </apply> </symResult> </symEval> <unitOverride xml:lang="zh_TW"> <placeholder xml:lang="zh_TW" /> </unitOverride> </eval> </math> </region>
2.
計算
sinh
並將結果傳遞至
asinh
，然後以符號方式與數值方式進行計算：
<region id="ID0ETV4KB" actualWidth="173.14666666666665" actualHeight="25.6" top="134.40000000000003" left="0" xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="16" xml:lang="zh_TW"> <eval xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50"> <apply xml:lang="zh_TW"> <id labels="FUNCTION" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">sinh</id> <id labels="VARIABLE" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">z</id> </apply> <unitOverride xml:lang="zh_TW"> <placeholder xml:lang="zh_TW" /> </unitOverride> </eval> <resultFormat xml:lang="zh_TW"> <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" xml:lang="zh_TW" /> </resultFormat> </math> </region>
<region id="ID0EFW4KB" actualWidth="259.17666666666668" actualHeight="51.158666666666669" top="172.8" left="0" xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="17" xml:lang="zh_TW"> <eval xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50"> <symEval xml:lang="zh_TW"> <apply xml:lang="zh_TW"> <id labels="FUNCTION" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">asinh</id> <apply xml:lang="zh_TW"> <id labels="FUNCTION" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">sinh</id> <id labels="VARIABLE" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">z</id> </apply> </apply> <command xml:lang="zh_TW"> <placeholder xml:lang="zh_TW" /> </command> <symResult xml:lang="zh_TW"> <apply xml:lang="zh_TW"> <plus xml:lang="zh_TW" /> <apply xml:lang="zh_TW"> <div xml:lang="zh_TW" /> <id labels="CONSTANT" xml:space="preserve" xml:lang="zh_TW">π</id> <real xml:lang="zh_TW">2</real> </apply> <imag symbol="i" xml:lang="zh_TW">1</imag> </apply> </symResult> </symEval> <unitOverride xml:lang="zh_TW"> <placeholder xml:lang="zh_TW" /> </unitOverride> </eval> <resultFormat xml:lang="zh_TW"> <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" xml:lang="zh_TW" /> </resultFormat> </math> </region>
一如預期，符號與數值結果均等於
z
的值。
3.
使用函數
cosh
與
acosh
重複上述步驟：
<region id="ID0EOZ4KB" actualWidth="175.42000000000002" actualHeight="25.6" top="211.20000000000005" left="0" xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="18" xml:lang="zh_TW"> <eval xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50"> <apply xml:lang="zh_TW"> <id labels="FUNCTION" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">cosh</id> <id labels="VARIABLE" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">z</id> </apply> <unitOverride xml:lang="zh_TW"> <placeholder xml:lang="zh_TW" /> </unitOverride> </eval> </math> </region>
<region id="ID0EA14KB" actualWidth="263.72333333333336" actualHeight="51.158666666666669" top="268.80000000000007" left="0" xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="19" xml:lang="zh_TW"> <eval xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50"> <symEval xml:lang="zh_TW"> <apply xml:lang="zh_TW"> <id labels="FUNCTION" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">acosh</id> <apply xml:lang="zh_TW"> <id labels="FUNCTION" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">cosh</id> <id labels="VARIABLE" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">z</id> </apply> </apply> <command xml:lang="zh_TW"> <placeholder xml:lang="zh_TW" /> </command> <symResult xml:lang="zh_TW"> <apply xml:lang="zh_TW"> <plus xml:lang="zh_TW" /> <apply xml:lang="zh_TW"> <div xml:lang="zh_TW" /> <id labels="CONSTANT" xml:space="preserve" xml:lang="zh_TW">π</id> <real xml:lang="zh_TW">2</real> </apply> <imag symbol="i" xml:lang="zh_TW">1</imag> </apply> </symResult> </symEval> <unitOverride xml:lang="zh_TW"> <placeholder xml:lang="zh_TW" /> </unitOverride> </eval> </math> </region>
4.
使用函數
tanh
與
atanh
重複上述步驟：
<region id="ID0E534KB" actualWidth="176.66666666666669" actualHeight="25.6" top="326.40000000000003" left="0" xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="20" xml:lang="zh_TW"> <eval xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50"> <apply xml:lang="zh_TW"> <id labels="FUNCTION" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">tanh</id> <id labels="VARIABLE" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">z</id> </apply> <unitOverride xml:lang="zh_TW"> <placeholder xml:lang="zh_TW" /> </unitOverride> </eval> </math> </region>
<region id="ID0EQ44KB" actualWidth="266.21666666666664" actualHeight="51.158666666666669" top="364.80000000000007" left="0" xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="21" xml:lang="zh_TW"> <eval xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50"> <symEval xml:lang="zh_TW"> <apply xml:lang="zh_TW"> <id labels="FUNCTION" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">atanh</id> <apply xml:lang="zh_TW"> <id labels="FUNCTION" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">tanh</id> <id labels="VARIABLE" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">z</id> </apply> </apply> <command xml:lang="zh_TW"> <placeholder xml:lang="zh_TW" /> </command> <symResult xml:lang="zh_TW"> <apply xml:lang="zh_TW"> <plus xml:lang="zh_TW" /> <apply xml:lang="zh_TW"> <div xml:lang="zh_TW" /> <id labels="CONSTANT" xml:space="preserve" xml:lang="zh_TW">π</id> <real xml:lang="zh_TW">2</real> </apply> <imag symbol="i" xml:lang="zh_TW">1</imag> </apply> </symResult> </symEval> <unitOverride xml:lang="zh_TW"> <placeholder xml:lang="zh_TW" /> </unitOverride> </eval> </math> </region>
5.
使用函數
coth
與
acoth
重複上述步驟：
<region id="ID0EOA5KB" actualWidth="175.42000000000002" actualHeight="25.6" top="422.40000000000009" left="0" xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="22" xml:lang="zh_TW"> <eval xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50"> <apply xml:lang="zh_TW"> <id labels="FUNCTION" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">coth</id> <id labels="VARIABLE" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">z</id> </apply> <unitOverride xml:lang="zh_TW"> <placeholder xml:lang="zh_TW" /> </unitOverride> </eval> </math> </region>
<region id="ID0EAB5KB" actualWidth="263.72333333333336" actualHeight="51.158666666666669" top="460.80000000000007" left="0" xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="23" xml:lang="zh_TW"> <eval xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50"> <symEval xml:lang="zh_TW"> <apply xml:lang="zh_TW"> <id labels="FUNCTION" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">acoth</id> <apply xml:lang="zh_TW"> <id labels="FUNCTION" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">coth</id> <id labels="VARIABLE" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">z</id> </apply> </apply> <command xml:lang="zh_TW"> <placeholder xml:lang="zh_TW" /> </command> <symResult xml:lang="zh_TW"> <apply xml:lang="zh_TW"> <plus xml:lang="zh_TW" /> <apply xml:lang="zh_TW"> <div xml:lang="zh_TW" /> <id labels="CONSTANT" xml:space="preserve" xml:lang="zh_TW">π</id> <real xml:lang="zh_TW">2</real> </apply> <imag symbol="i" xml:lang="zh_TW">1</imag> </apply> </symResult> </symEval> <unitOverride xml:lang="zh_TW"> <placeholder xml:lang="zh_TW" /> </unitOverride> </eval> </math> </region>
6.
使用函數
sech
與
asech
重複上述步驟：
<region id="ID0E5D5KB" actualWidth="174.54000000000002" actualHeight="25.6" top="518.40000000000009" left="0" xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="24" xml:lang="zh_TW"> <eval xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50"> <apply xml:lang="zh_TW"> <id labels="FUNCTION" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">sech</id> <id labels="VARIABLE" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">z</id> </apply> <unitOverride xml:lang="zh_TW"> <placeholder xml:lang="zh_TW" /> </unitOverride> </eval> <resultFormat xml:lang="zh_TW"> <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" xml:lang="zh_TW" /> </resultFormat> </math> </region>
<region id="ID0EQE5KB" actualWidth="261.96333333333331" actualHeight="51.158666666666669" top="556.80000000000007" left="0" xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="25" xml:lang="zh_TW"> <eval xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50"> <symEval xml:lang="zh_TW"> <apply xml:lang="zh_TW"> <id labels="FUNCTION" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">asech</id> <apply xml:lang="zh_TW"> <id labels="FUNCTION" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">sech</id> <id labels="VARIABLE" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">z</id> </apply> </apply> <command xml:lang="zh_TW"> <placeholder xml:lang="zh_TW" /> </command> <symResult xml:lang="zh_TW"> <apply xml:lang="zh_TW"> <plus xml:lang="zh_TW" /> <apply xml:lang="zh_TW"> <div xml:lang="zh_TW" /> <id labels="CONSTANT" xml:space="preserve" xml:lang="zh_TW">π</id> <real xml:lang="zh_TW">2</real> </apply> <imag symbol="i" xml:lang="zh_TW">1</imag> </apply> </symResult> </symEval> <unitOverride xml:lang="zh_TW"> <placeholder xml:lang="zh_TW" /> </unitOverride> </eval> <resultFormat xml:lang="zh_TW"> <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" xml:lang="zh_TW" /> </resultFormat> </math> </region>
7.
使用函數
csch
與
acsch
重複上述步驟：
<region id="ID0EOH5KB" actualWidth="174.54000000000002" actualHeight="25.6" top="614.40000000000009" left="0" xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="26" xml:lang="zh_TW"> <eval xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50"> <apply xml:lang="zh_TW"> <id labels="FUNCTION" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">csch</id> <id labels="VARIABLE" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">z</id> </apply> <unitOverride xml:lang="zh_TW"> <placeholder xml:lang="zh_TW" /> </unitOverride> </eval> <resultFormat xml:lang="zh_TW"> <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" xml:lang="zh_TW" /> </resultFormat> </math> </region>
<region id="ID0EAI5KB" actualWidth="261.96333333333331" actualHeight="51.158666666666669" top="652.80000000000007" left="0" xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="27" xml:lang="zh_TW"> <eval xml:lang="zh_TW" xmlns="http://schemas.mathsoft.com/math50"> <symEval xml:lang="zh_TW"> <apply xml:lang="zh_TW"> <id labels="FUNCTION" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">acsch</id> <apply xml:lang="zh_TW"> <id labels="FUNCTION" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">csch</id> <id labels="VARIABLE" xml:space="preserve" xml:lang="zh_TW" label-is-contextual="true">z</id> </apply> </apply> <command xml:lang="zh_TW"> <placeholder xml:lang="zh_TW" /> </command> <symResult xml:lang="zh_TW"> <apply xml:lang="zh_TW"> <plus xml:lang="zh_TW" /> <apply xml:lang="zh_TW"> <div xml:lang="zh_TW" /> <id labels="CONSTANT" xml:space="preserve" xml:lang="zh_TW">π</id> <real xml:lang="zh_TW">2</real> </apply> <imag symbol="i" xml:lang="zh_TW">1</imag> </apply> </symResult> </symEval> <unitOverride xml:lang="zh_TW"> <placeholder xml:lang="zh_TW" /> </unitOverride> </eval> <resultFormat xml:lang="zh_TW"> <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" xml:lang="zh_TW" /> </resultFormat> </math> </region>
複製運算式
