Functions
>
Trigonometric, Log, and Exponential
> Example: Inverse Trigonometric Functions
Example: Inverse Trigonometric Functions
Use inverse trigonometric functions to get the value, in radians, of various trigonometric functions.
1.
Symbolically evaluate functions
sin
and
cos
.
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<region id="ID0EI3RDB" actualWidth="88.920000000000016" actualHeight="51.158666666666669" top="38.400000000000006" left="172.8" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="31"> <symEval xmlns="http://schemas.mathsoft.com/math50"> <apply> <id labels="FUNCTION" label-is-contextual="true" xml:space="preserve">cos</id> <apply> <div /> <id labels="CONSTANT" label-is-contextual="true" xml:space="preserve">π</id> <real>2</real> </apply> </apply> <command> <placeholder /> </command> <symResult> <real>0</real> </symResult> </symEval> <resultFormat> <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" /> </resultFormat> </math> </region>
2.
Use the returned values to symbolically evaluate functions
acos
and
asin
.
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<region id="ID0EE6RDB" actualWidth="96.913333333333355" actualHeight="51.158666666666669" top="96.000000000000014" left="172.8" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="33"> <symEval xmlns="http://schemas.mathsoft.com/math50"> <apply> <id labels="FUNCTION" label-is-contextual="true" xml:space="preserve">acos</id> <real>0</real> </apply> <command> <placeholder /> </command> <symResult> <apply> <div /> <id labels="CONSTANT" xml:space="preserve">π</id> <real>2</real> </apply> </symResult> </symEval> <resultFormat> <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" /> </resultFormat> </math> </region>
The returned values are in radians.
3.
Evaluate the same functions numerically.
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<region id="ID0EGBSDB" actualWidth="120.49333333333334" actualHeight="25.6" top="153.60000000000002" left="172.8" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="35"> <eval xmlns="http://schemas.mathsoft.com/math50"> <apply> <id labels="FUNCTION" label-is-contextual="true" xml:space="preserve">acos</id> <real>0</real> </apply> <unitOverride> <placeholder /> </unitOverride> </eval> <resultFormat> <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" /> </resultFormat> </math> </region>
4.
Repeat this comparison for functions
cot
,
acot
,
sec
,
asec
,
csc
and
acsc
using different values.
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<region id="ID0ELHSDB" actualWidth="116.69600031296414" actualHeight="53.445333527326589" top="230.40000000000003" left="172.8" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="37"> <symEval xmlns="http://schemas.mathsoft.com/math50"> <apply> <id labels="FUNCTION" label-is-contextual="true" xml:space="preserve">acot</id> <apply> <div /> <apply> <nthRoot /> <placeholder /> <real>3</real> </apply> <real>3</real> </apply> </apply> <command> <placeholder /> </command> <symResult> <apply> <div /> <id labels="CONSTANT" xml:space="preserve">π</id> <real>3</real> </apply> </symResult> </symEval> <resultFormat> <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" /> </resultFormat> </math> </region>
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<region id="ID0EYISDB" actualWidth="93.783333333333346" actualHeight="39.2" top="307.20000000000005" left="19.200000000000003" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="39"> <symEval xmlns="http://schemas.mathsoft.com/math50"> <apply> <id xml:space="preserve">sec</id> <id labels="CONSTANT" label-is-contextual="true" xml:space="preserve">π</id> </apply> <command> <placeholder /> </command> <symResult> <real>-1</real> </symResult> </symEval> <resultFormat> <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" /> </resultFormat> </math> </region>
<region id="ID0EMJSDB" actualWidth="101.98333333333335" actualHeight="39.2" top="307.20000000000005" left="172.8" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="40"> <symEval xmlns="http://schemas.mathsoft.com/math50"> <apply> <id labels="FUNCTION" xml:space="preserve">asec</id> <real>-1</real> </apply> <command> <placeholder /> </command> <symResult> <id labels="CONSTANT" xml:space="preserve">π</id> </symResult> </symEval> <resultFormat> <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" /> </resultFormat> </math> </region>
<region id="ID0EAKSDB" actualWidth="130.36333333333334" actualHeight="25.6" top="307.20000000000005" left="345.6" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="41"> <eval xmlns="http://schemas.mathsoft.com/math50"> <apply> <id labels="FUNCTION" xml:space="preserve">asec</id> <real>-1</real> </apply> <unitOverride> <placeholder /> </unitOverride> </eval> <resultFormat> <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" /> </resultFormat> </math> </region>
<region id="ID0EZKSDB" actualWidth="88.04" actualHeight="51.158666666666669" top="384.00000000000006" left="19.200000000000003" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="42"> <symEval xmlns="http://schemas.mathsoft.com/math50"> <apply> <id labels="FUNCTION" label-is-contextual="true" xml:space="preserve">csc</id> <apply> <div /> <id labels="CONSTANT" label-is-contextual="true" xml:space="preserve">π</id> <real>2</real> </apply> </apply> <command> <placeholder /> </command> <symResult> <real>1</real> </symResult> </symEval> <resultFormat> <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" /> </resultFormat> </math> </region>
<region id="ID0ENLSDB" actualWidth="96.033333333333331" actualHeight="51.158666666666669" top="384.00000000000006" left="172.8" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="43"> <symEval xmlns="http://schemas.mathsoft.com/math50"> <apply> <id labels="FUNCTION" xml:space="preserve">acsc</id> <real>1</real> </apply> <command> <placeholder /> </command> <symResult> <apply> <div /> <id labels="CONSTANT" xml:space="preserve">π</id> <real>2</real> </apply> </symResult> </symEval> <resultFormat> <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" /> </resultFormat> </math> </region>
<region id="ID0EBMSDB" actualWidth="119.61333333333334" actualHeight="25.6" top="384.00000000000006" left="345.6" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="44"> <eval xmlns="http://schemas.mathsoft.com/math50"> <apply> <id labels="FUNCTION" label-is-contextual="true" xml:space="preserve">acsc</id> <real>1</real> </apply> <unitOverride> <placeholder /> </unitOverride> </eval> </math> </region>
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Related Topics
Inverse Trigonometric Functions
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