Identidades Trigonom\303\251tricas: Adi\303\247\303\243o e Subtra\303\247\303\243o de \303\202ngulos Conceito Principal Existem muitas identidades trigonom\303\251tricas usadas em matem\303\241tica, entre eles as f\303\263rmulas de adi\303\247\303\243o e subtra\303\247\303\243o de \303\242ngulos. Estas f\303\263rmulas seguem abaixo:
Adi\303\247\303\243o de \303\202ngulos ou Subtra\303\247\303\243o de \303\202ngulos LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbWlHRiQ2KFErSWRlbnRpZGFkZUYnLyUnZmFtaWx5R1EsRGVqYVZ1flNhbnNGJy8lJXNpemVHUSMxMUYnLyUnaXRhbGljR1EmZmFsc2VGJy8lK2V4ZWN1dGFibGVHRjcvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkjbW9HRiQ2MFEifkYnRi9GMkY4RjovJSZmZW5jZUdGNy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZRLUYsNihRLEVxdWl2YWxlbnRlRidGL0YyRjVGOEY6Ri9GMkY4Rjo= 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEkY29zRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZXhlY3V0YWJsZUdGMS8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSShtZmVuY2VkR0YkNiUtRiM2Jy1GLDYmUSJBRicvRjBRJXRydWVGJ0YyL0Y1USdpdGFsaWNGJy1JI21vR0YkNi5RIitGJ0YyRjQvJSZmZW5jZUdGMS8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0YxLyUqc3ltbWV0cmljR0YxLyUobGFyZ2VvcEdGMS8lLm1vdmFibGVsaW1pdHNHRjEvJSdhY2NlbnRHRjEvJSdsc3BhY2VHUSwwLjIyMjIyMjJlbUYnLyUncnNwYWNlR0ZXLUYsNiZRIkJGJ0Y/RjJGQUYyRjRGMkY0RjJGNA== 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEkdGFuRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZXhlY3V0YWJsZUdGMS8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSShtZmVuY2VkR0YkNiUtRiM2Jy1GLDYmUSJBRicvRjBRJXRydWVGJ0YyL0Y1USdpdGFsaWNGJy1JI21vR0YkNi5RIitGJ0YyRjQvJSZmZW5jZUdGMS8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0YxLyUqc3ltbWV0cmljR0YxLyUobGFyZ2VvcEdGMS8lLm1vdmFibGVsaW1pdHNHRjEvJSdhY2NlbnRHRjEvJSdsc3BhY2VHUSwwLjIyMjIyMjJlbUYnLyUncnNwYWNlR0ZXLUYsNiZRIkJGJ0Y/RjJGQUYyRjRGMkY0RjJGNA== 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEkdGFuRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZXhlY3V0YWJsZUdGMS8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSShtZmVuY2VkR0YkNiUtRiM2Jy1GLDYmUSJBRicvRjBRJXRydWVGJ0YyL0Y1USdpdGFsaWNGJy1JI21vR0YkNi5RKCZtaW51cztGJ0YyRjQvJSZmZW5jZUdGMS8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0YxLyUqc3ltbWV0cmljR0YxLyUobGFyZ2VvcEdGMS8lLm1vdmFibGVsaW1pdHNHRjEvJSdhY2NlbnRHRjEvJSdsc3BhY2VHUSwwLjIyMjIyMjJlbUYnLyUncnNwYWNlR0ZXLUYsNiZRIkJGJ0Y/RjJGQUYyRjRGMkY0RjJGNA== 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
As seguintes quest\303\265es s\303\243o focadas em adi\303\247\303\265es de \303\242ngulos. Ambas as identidades para LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEkc2luRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZXhlY3V0YWJsZUdGMS8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSShtZmVuY2VkR0YkNiUtRiM2Jy1GLDYmUSJBRicvRjBRJXRydWVGJ0YyL0Y1USdpdGFsaWNGJy1JI21vR0YkNi5RIitGJ0YyRjQvJSZmZW5jZUdGMS8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0YxLyUqc3ltbWV0cmljR0YxLyUobGFyZ2VvcEdGMS8lLm1vdmFibGVsaW1pdHNHRjEvJSdhY2NlbnRHRjEvJSdsc3BhY2VHUSwwLjIyMjIyMjJlbUYnLyUncnNwYWNlR0ZXLUYsNiZRIkJGJ0Y/RjJGQUYyRjRGMkY0RjJGNA== e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEkY29zRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZXhlY3V0YWJsZUdGMS8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSShtZmVuY2VkR0YkNiUtRiM2Jy1GLDYmUSJBRicvRjBRJXRydWVGJ0YyL0Y1USdpdGFsaWNGJy1JI21vR0YkNi5RIitGJ0YyRjQvJSZmZW5jZUdGMS8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0YxLyUqc3ltbWV0cmljR0YxLyUobGFyZ2VvcEdGMS8lLm1vdmFibGVsaW1pdHNHRjEvJSdhY2NlbnRHRjEvJSdsc3BhY2VHUSwwLjIyMjIyMjJlbUYnLyUncnNwYWNlR0ZXLUYsNiZRIkJGJ0Y/RjJGQUYyRjRGMkY0RjJGNA== podem ser derivadas usando geometria como mostrado abaixo. Selecione o seletor apropriado e clique "Pr\303\263ximo" para ver, passo a passo, como a identidade \303\251 derivada. AngleAddition :- Click();AngleAddition :- Click();AngleAddition:-Next(); 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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= Quest\303\265es 1. Usando as identidades na tabela acima, determine o valor de sin(75\302\260). 2. Prove que LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbWlHRiQ2JlEkdGFuRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZXhlY3V0YWJsZUdGMS8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSShtZmVuY2VkR0YkNiUtRiM2Jy1GLDYmUSJBRicvRjBRJXRydWVGJ0YyL0Y1USdpdGFsaWNGJy1JI21vR0YkNi5RIitGJ0YyRjQvJSZmZW5jZUdGMS8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0YxLyUqc3ltbWV0cmljR0YxLyUobGFyZ2VvcEdGMS8lLm1vdmFibGVsaW1pdHNHRjEvJSdhY2NlbnRHRjEvJSdsc3BhY2VHUSwwLjIyMjIyMjJlbUYnLyUncnNwYWNlR0ZXLUYsNiZRIkJGJ0Y/RjJGQUYyRjRGMkY0LUZENi5RIj1GJ0YyRjRGR0ZJRktGTUZPRlFGUy9GVlEsMC4yNzc3Nzc4ZW1GJy9GWUZbby1JJm1mcmFjR0YkNigtRiM2KkYrLUY4NiUtRiM2JUY8RjJGNEYyRjRGQ0YrLUY4NiUtRiM2JUZaRjJGNEYyRjQtRiw2I1EhRidGMkY0LUYjNiotSSNtbkdGJDYlUSIxRidGMkY0LUZENi5RKCZtaW51cztGJ0YyRjRGR0ZJRktGTUZPRlFGU0ZVRlhGK0Zib0YrRmZvRjJGNC8lLmxpbmV0aGlja25lc3NHRmJwLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRmpwLyUpYmV2ZWxsZWRHRjEtRkQ2LlEiLkYnRjJGNEZHRklGS0ZNRk9GUUZTL0ZWUSYwLjBlbUYnL0ZZRmNxRjJGNA== LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
<Text-field bookmark="bkmrk0" style="Heading 1" bold="false" italic="true" size="12" layout="Heading 1"><Font size="12" bold="true" encoding="UTF-8" italic="true">Solu\303\247\303\265es</Font></Text-field> LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=
<Text-field bookmark="bkmrk1" style="Heading 2" italic="true" size="12" layout="Heading 2"><Font size="12" encoding="UTF-8" italic="true">Solu\303\247\303\243o 1</Font></Text-field> Use a identidade 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 para determinar o valor de sin(75\302\260): Primeiramente, note que 45\302\260 + 30\302\260 = 75\302\260. 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
<Text-field bookmark="bkmrk2" style="Heading 2" size="12" layout="Heading 2"><Font size="12" encoding="UTF-8" italic="true">Solu\303\247\303\243o 2</Font></Text-field> Primeiramente, note que: 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 Substituindo as identidades para LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEkc2luRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZXhlY3V0YWJsZUdGMS8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSShtZmVuY2VkR0YkNiUtRiM2Jy1GLDYmUSJBRicvRjBRJXRydWVGJ0YyL0Y1USdpdGFsaWNGJy1JI21vR0YkNi5RIitGJ0YyRjQvJSZmZW5jZUdGMS8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0YxLyUqc3ltbWV0cmljR0YxLyUobGFyZ2VvcEdGMS8lLm1vdmFibGVsaW1pdHNHRjEvJSdhY2NlbnRHRjEvJSdsc3BhY2VHUSwwLjIyMjIyMjJlbUYnLyUncnNwYWNlR0ZXLUYsNiZRIkJGJ0Y/RjJGQUYyRjRGMkY0RjJGNA== e 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 obtemos: 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 Agora, divida cada termo por LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2KS1GLDYmUSRjb3NGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJStleGVjdXRhYmxlR0Y2LyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JKG1mZW5jZWRHRiQ2JS1GIzYlLUYsNiZRIkFGJy9GNVEldHJ1ZUYnRjcvRjpRJ2l0YWxpY0YnRjdGOUY3RjlGMS1GPTYlLUYjNiUtRiw2JlEiQkYnRkRGN0ZGRjdGOUY3RjlGK0Y3RjlGK0Y3Rjk=: 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 Simplificando: 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 Finalmente obtemos: 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
JSFH LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=