Problemas de trigonometriaE. OezgenEmail: erol-oez@hotmail.deV. epis\303\263dio
Problema:
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYzLUkrbXVuZGVyb3ZlckdGJDYnLUkjbW9HRiQ2LVEmJlN1bTtGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJnVuc2V0RicvJSpzZXBhcmF0b3JHRjcvJSlzdHJldGNoeUdRJXRydWVGJy8lKnN5bW1ldHJpY0dGNy8lKGxhcmdlb3BHRjwvJS5tb3ZhYmxlbGltaXRzR0Y8LyUnYWNjZW50R0Y3LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMTY2NjY2N2VtRictRiM2Ji1JI21pR0YkNiVRImtGJy8lJ2l0YWxpY0dGPC9GM1EnaXRhbGljRictRi82LVEiPUYnRjIvRjZRJmZhbHNlRicvRjlGWS9GO0ZZL0Y+RlkvRkBGWS9GQkZZL0ZERlkvRkZRLDAuMjc3Nzc3OGVtRicvRklGW28tSSNtbkdGJDYkUSIxRidGMkYyLUYjNiQtRk42JVEibkYnRlFGU0YyRmluLyUsYWNjZW50dW5kZXJHRlktSSVtc3VwR0YkNiUtRk42JVEkY29zRicvRlJGWUYyLUYjNiUtRl5vNiRRIjJGJ0YyRlFGUy8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRictSShtZmVuY2VkR0YkNiQtRiM2J0ZNLUYvNi1RIn5GJ0YyRlhGWkZlbkZmbkZnbkZobkZpbkZFL0ZJRkctRk42JVEieEYnRlFGUy8lK2V4ZWN1dGFibGVHRllGMkYyRlVGaG8tRmhwNiQtRiM2JUZgcUZjcUYyRjItRi82LVEiK0YnRjJGWEZaRmVuRmZuRmduRmhuRmluL0ZGUSwwLjIyMjIyMjJlbUYnL0ZJRl1yRmhvLUZocDYkLUYjNidGYXBGXHFGYHFGY3FGMkYyRmlxLUYvNi1RIy4uRidGMkZYRlpGZW5GZm5GZ25GaG5GaW5GXHJGX3FGY3JGaXFGaG8tRmhwNiQtRiM2J0Zjb0ZccUZgcUZjcUYyRjJGY3FGMg== (*)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 (**) voc\303\252 calculou o total deles. (**) fazendo uso da 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 a f\303\263rmula.JSFH
Solu\303\247\303\243o:\303\211 poss\303\255vel calcular as somas pesquisadas diretamente com o Maple.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
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=seja encontrado.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 Para provar a f\303\263rmula, ambos os lados de (4) LUklbXN1cEc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUklbXJvd0dGJDYkLUkjbW5HRiQ2JVEiMkYnRjIvRjZRJ25vcm1hbEYnRj8vJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYn dividido por LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JlEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEtJlJpZ2h0QXJyb3c7RidGMi9GNlEnbm9ybWFsRicvJSZmZW5jZUdGNC8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0YxLyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZOLUkjbW5HRiQ2JVEiMEYnRjJGPEYyRjw=Vamos calcular os limites para.
Lado 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, 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, 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,.... ,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, ......desde o limite do lado esquerdo 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 \303\251.JSFHNesse 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obtido.Problema:
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voc\303\252 calculou o total deles.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 fazendo uso da 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Prove a f\303\263rmula.LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
Deixo a solu\303\247\303\243o deste problema para o leitor como uma pr\303\241tica.Problema:
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voc\303\252 calculou o total deles.JSFH
Solu\303\247\303\243o:Os valores solicitados tamb\303\251m podem ser obtidos diretamente com a Maple.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Comente:Essas somas s\303\243o calculadas nas f\303\263rmulas (***) e (****) fornecidas em Problemas de trigonometria (Se\303\247\303\243o IV). LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiYkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn em vez de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JlEiYkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEiK0YnRjIvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EsMC4yMjIyMjIyZW1GJy8lJ3JzcGFjZUdGTi1GLDYmUScmIzk2MDtGJy9GMEY0RjJGPEYyRjw= Tamb\303\251m \303\251 poss\303\255vel obt\303\252-lo colocando-o.
Por exemplo, na f\303\263rmula (***) dada na (Se\303\247\303\243o IV) LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JlEibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEiPUYnRjIvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTi1JI21uR0YkNiVRIzEwRidGMkY8RjJGPA== de qualquer 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por outro 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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEjaXNGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiQtRiM2KS1GLDYjUSFGJy1JKG1hY3Rpb25HRiQ2JS1JKm12ZXJiYXRpbUdGJDYjUWddbCooLUkkY29zRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMsKComIyIiKiIiIyIiIkkiYkc2IiIiIiIiIiomIyIiKiIiIyIiIkkjUGlHJSpwcm90ZWN0ZWRHIiIiIiIiSSJhRzYiIiIiIiIiLUkkc2luRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMsJiomIiImIiIiSSJiRzYiIiIiIiIiKiYiIiYiIiJJI1BpRyUqcHJvdGVjdGVkRyIiIiIiIiIiIi1JJHNpbkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjLCYqJiMiIiIiIiMiIiJJImJHNiIiIiIiIiIqJiMiIiIiIiMiIiJJI1BpRyUqcHJvdGVjdGVkRyIiIiIiIiEiIkYnLyUrYWN0aW9udHlwZUdROm1hcGxlc29mdC5jb206bGFiZWwoTDc0MilGJy8lJXZpZXdHUSZsYWJlbEYnLUkjbW9HRiQ2LVEiPUYnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGUi8lKXN0cmV0Y2h5R0ZSLyUqc3ltbWV0cmljR0ZSLyUobGFyZ2VvcEdGUi8lLm1vdmFibGVsaW1pdHNHRlIvJSdhY2NlbnRHRlIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0Zbby1GPjYlLUZBNiNRZF5sKiYsKi1JJGNvc0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjLCZJImFHNiIiIiIqJiIiKiIiIkkiYkc2IiIiIiIiIiEiIi1JJGNvc0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjLCZJImFHNiIiIiIqJiIjNSIiIkkiYkc2IiIiIiIiIiEiIi1JJGNvc0c2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjLCZJImFHNiIiIiJJImJHNiIhIiIiIiItSSRjb3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2I0kiYUc2IiIiIiIiIiwmIiIjIiIiKiYiIiMiIiItSSRjb3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2I0kiYkc2IiIiIiIiIiEiIkYnL0ZFUTptYXBsZXNvZnQuY29tOmxhYmVsKEw3NjIpRidGR0Y6LyUrZXhlY3V0YWJsZUdGUkZORk5GZW9GTg==seria.