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<Text-field style="Heading 1" layout="Normal"><Font encoding="UTF-8">fun\303\247\303\243o hiperb\303\263lica,</Font></Text-field>
<Text-field style="Text" layout="Normal"><Font italic="true">s.</Font><Font encoding="UTF-8"> de um grupo de fun\303\247\303\265es de um \303\242ngulo originalmente definido em termos das </Font><Hyperlink linktarget="Dictionary:Definition/trigonometricfunction" hyperlink="true"><Font style="Dictionary Hyperlink" family="Times New Roman" encoding="UTF-8">fun\303\247\303\265es trigonom\303\251tricas</Font></Hyperlink> ou em termos de <Hyperlink linktarget="Dictionary:Definition/exponentialfunction" hyperlink="true"><Font style="Dictionary Hyperlink" family="Times New Roman" encoding="UTF-8">fun\303\247\303\265es exponenciais</Font></Hyperlink><Font encoding="UTF-8">. As fun\303\247\303\265es hiperb\303\263licas prim\303\241rias s\303\243o </Font><Hyperlink linktarget="Dictionary:Definition/sinh" hyperlink="true"><Font style="Dictionary Hyperlink" family="Times New Roman">senh</Font></Hyperlink> (<Font encoding="UTF-8" italic="true">seno hiperb\303\263lico</Font>) definido como </Text-field>
<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation> = <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkmbWZyYWNHRiQ2KC1GIzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1JJW1zdXBHRiQ2JS1GMTYlUSJlRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYxNiVRInpGJ0Y8Rj8vJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnLUkjbW9HRiQ2LVEoJm1pbnVzO0YnL0ZAUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGUC8lKXN0cmV0Y2h5R0ZQLyUqc3ltbWV0cmljR0ZQLyUobGFyZ2VvcEdGUC8lLm1vdmFibGVsaW1pdHNHRlAvJSdhY2NlbnRHRlAvJSdsc3BhY2VHUSwwLjIyMjIyMjJlbUYnLyUncnNwYWNlR0Zpbi1GNzYlRjktRiM2JS1GSTYtUSomdW1pbnVzMDtGJ0ZMRk5GUUZTRlVGV0ZZRmVuRmduRmpuRkJGTEZFRkxGMEZMLUYjNiQtSSNtbkdGJDYkUSIyRidGTEZMLyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZecC8lKWJldmVsbGVkR0ZQRkw=">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</Equation>, 
e <Hyperlink linktarget="Dictionary:Definition/cosh" hyperlink="true"><Font style="Dictionary Hyperlink" family="Times New Roman">cosh</Font></Hyperlink> (<Font encoding="UTF-8" italic="true">cosseno hiperb\303\263lico</Font>), definido como </Text-field>
<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2KEYrLUYjNiYtRiw2JVElY29zaEYnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYtUTEmSW52aXNpYmxlVGltZXM7RidGOS8lJmZlbmNlR0Y4LyUqc2VwYXJhdG9yR0Y4LyUpc3RyZXRjaHlHRjgvJSpzeW1tZXRyaWNHRjgvJShsYXJnZW9wR0Y4LyUubW92YWJsZWxpbWl0c0dGOC8lJ2FjY2VudEdGOC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRlAtRiw2JVEiekYnL0Y3USV0cnVlRicvRjpRJ2l0YWxpY0YnRjktRj02LVEiPUYnRjlGQEZCRkRGRkZIRkpGTC9GT1EsMC4yNzc3Nzc4ZW1GJy9GUkZobi1GIzYmLUYsNiVRJGNvc0YnRjZGOS1GPTYtUTAmQXBwbHlGdW5jdGlvbjtGJ0Y5RkBGQkZERkZGSEZKRkxGTkZRLUkobWZlbmNlZEdGJDYkLUYjNiZGKy1GIzYmLUYsNiVRImlGJ0ZWRlhGPEZTRjlGK0Y5RjlGOUYrRjlGK0Y5">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</Equation> = <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkmbWZyYWNHRiQ2KC1GIzYmLUkjbWlHRiQ2I1EhRictRiM2Ji1JJW1zdXBHRiQ2JS1GMTYlUSJlRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYxNiVRInpGJ0Y8Rj8vJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnLUkjbW9HRiQ2LVEiK0YnL0ZAUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGUC8lKXN0cmV0Y2h5R0ZQLyUqc3ltbWV0cmljR0ZQLyUobGFyZ2VvcEdGUC8lLm1vdmFibGVsaW1pdHNHRlAvJSdhY2NlbnRHRlAvJSdsc3BhY2VHUSwwLjIyMjIyMjJlbUYnLyUncnNwYWNlR0Zpbi1GNzYlRjktRiM2JS1GSTYtUSomdW1pbnVzMDtGJ0ZMRk5GUUZTRlVGV0ZZRmVuRmduRmpuRkJGTEZFRkxGMEZMLUYjNiQtSSNtbkdGJDYkUSIyRidGTEZMLyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZecC8lKWJldmVsbGVkR0ZQRkw=">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</Equation> 
para  <Font italic="true">z </Font>complexo; <Hyperlink linktarget="Dictionary:Definition/tanh" hyperlink="true"><Font style="Dictionary Hyperlink" family="Times New Roman">tanh</Font></Hyperlink> (<Font encoding="UTF-8" italic="true">tangente hiperb\303\263lica</Font><Font encoding="UTF-8">) \303\251 definida como a raz\303\243o do seno por cosseno. Os rec\303\255procos destas tr\303\252s fun\303\247\303\265es s\303\243o respectivamente </Font><Hyperlink linktarget="Dictionary:Definition/csch" hyperlink="true"><Font style="Dictionary Hyperlink" family="Times New Roman">csch</Font></Hyperlink> (<Font encoding="UTF-8" italic="true">cossecante hiperb\303\263lica</Font>), <Hyperlink linktarget="Dictionary:Definition/sech" hyperlink="true"><Font style="Dictionary Hyperlink" family="Times New Roman">sech</Font></Hyperlink> (<Font italic="true">secante <Font encoding="UTF-8">hiperb\303\263lica</Font></Font>), e <Hyperlink linktarget="Dictionary:Definition/coth" hyperlink="true"><Font style="Dictionary Hyperlink" family="Times New Roman">coth</Font></Hyperlink> (<Font italic="true">cotangente <Font encoding="UTF-8">hiperb\303\263lica</Font></Font><Font encoding="UTF-8">). Suas inversas s\303\243o </Font><Hyperlink linktarget="Dictionary:Definition/arcsinh" hyperlink="true"><Font style="Dictionary Hyperlink" family="Times New Roman">arcsenh</Font></Hyperlink>, <Hyperlink linktarget="Dictionary:Definition/arccosh" hyperlink="true"><Font style="Dictionary Hyperlink" family="Times New Roman">arccosh</Font></Hyperlink>, <Hyperlink linktarget="Dictionary:Definition/arctanh" hyperlink="true"><Font style="Dictionary Hyperlink" family="Times New Roman">arctanh</Font></Hyperlink><Font encoding="UTF-8">, etc. As fun\303\247\303\265es hiperb\303\263licas satisfazem a identidade </Font></Text-field>
<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation>, 
<Font encoding="UTF-8">ent\303\243o, o ponto (cosh</Font><Font family="MaplePi">a</Font>, senh<Font family="MaplePi">a</Font><Font encoding="UTF-8">) fica sobre a hip\303\251rbole retangular </Font></Text-field>
<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2J0YrLUYjNihGKy1GIzYkLUklbXN1cEdGJDYlLUYsNiVRInhGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtbkdGJDYkUSIyRicvRj9RJ25vcm1hbEYnLyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJ0ZFLUkjbW9HRiQ2LVEoJm1pbnVzO0YnRkUvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRlAvJSlzdHJldGNoeUdGUC8lKnN5bW1ldHJpY0dGUC8lKGxhcmdlb3BHRlAvJS5tb3ZhYmxlbGltaXRzR0ZQLyUnYWNjZW50R0ZQLyUnbHNwYWNlR1EsMC4yMjIyMjIyZW1GJy8lJ3JzcGFjZUdGaW4tRiM2JC1GNjYlLUYsNiVRInlGJ0Y7Rj5GQUZHRkVGK0ZFLUZLNi1RIj1GJ0ZFRk5GUUZTRlVGV0ZZRmVuL0ZoblEsMC4yNzc3Nzc4ZW1GJy9GW29GZ28tRkI2JFEiMUYnRkVGRUYrRkU=">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</Equation>, 
<Font encoding="UTF-8">como mostrado abaixo; isso \303\251 an\303\241logo \303\240 identidade trigonom\303\251trica sen</Font><Font superscript="true">2</Font><Font family="MaplePi">q</Font> + cos<Font superscript="true">2</Font><Font family="MaplePi">q</Font> = 1, onde o ponto (cos<Font family="MaplePi">q</Font>, sin<Font family="MaplePi">q</Font><Font encoding="UTF-8">) fica sobre o c\303\255rculo unit\303\241rio. No caso hiperb\303\263lico, o par\303\242metro </Font><Font family="MaplePi">a </Font><Font encoding="UTF-8"> \303\251 duas vezes a \303\241rea fechada pelo eixo-</Font><Font italic="true">x</Font><Font encoding="UTF-8">, o arco da hip\303\251rbole unit\303\241ria entre o v\303\251rtice e (cosh</Font><Font family="MaplePi">a</Font>, sinh<Font family="MaplePi">a</Font>) e a linha que junta este ponto a origem, como mostrado na figura, onde 
       cosh<Font superscript="true">-1</Font> <Font italic="true">x</Font>  =  senh<Font superscript="true">-1</Font> <Font italic="true">y</Font>  = <Font family="MaplePi">a</Font>. 
<Font encoding="UTF-8">Em geral, as fun\303\247\303\265es hiperb\303\263licas satisfazem todas as identididade trigonom\303\251tricas exceto para mudan\303\247as no sinal de termos de segundo grau em senh. </Font></Text-field>
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<Text-field style="Text" layout="Normal" alignment="centred"><Font bold="true" encoding="UTF-8">Fun\303\247\303\265es hiperb\303\263licas.</Font> (cosh<Font family="MaplePi">a</Font>, senh<Font family="MaplePi">a</Font><Font encoding="UTF-8">) descreve a hip\303\251rbole.</Font></Text-field>
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</Worksheet>