questões de trigonometria
Anexos:
JBRY:
Esta dividindo as perguntas?
como assim?
A ideia que o Lucas deu ai agora.
professor eu não sei como dividir já tentei e não conseguir
Escreva uma ou duas em cada folha e poste novamente com certeza vai ser resolvido mais rápido.
vou tentar
professor vai lá no meu perfil eu coloquei duas
Posta os outros exercício separados.
http://brainly.com.br/tarefa/4463927
professor responde essas
Soluções para a tarefa
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Boa tarde Gerlan!
Solução!
Exercicio 83
![5sec(x)-3tan^{2}x=1\\\\\\
5 \dfrac{1}{cos(x)}-3 \dfrac{sen^{2}(x) }{cos^{2} (x) }=1\\\\\\
\dfrac{5cos(x)}{cos^{2}(x) } -3 \dfrac{sen^{2}(x) }{cos^{2} (x) }= \dfrac{cos ^{2}(x) }{cos^{2}(x)} \\\\\\\
\dfrac{ [5cos(x)-3sen^{2}x-cos^{2}x]}{cos^{2} (x)} \\\\\\\
\dfrac{5cos(x)-3[1-cos^{2}x]-cos^{2}x}{ cos^{2}(x) } \\\\\\\
\dfrac{5cos(x)-3+3cos^{2}x-cos^{2}x }{2cos^{2}x }\\\\\\\
2cos^{2}x+5cos(x)\dfrac{-3cos^{2}x }{cos^{2}x } \\\\\\\
2cos^{2}x+5cos(x)-3=0\\\\
Uma ~~equacao~~ do ~~segundo ~~grau.](https://tex.z-dn.net/?f=5sec%28x%29-3tan%5E%7B2%7Dx%3D1%5C%5C%5C%5C%5C%5C%0A5+%5Cdfrac%7B1%7D%7Bcos%28x%29%7D-3+%5Cdfrac%7Bsen%5E%7B2%7D%28x%29+%7D%7Bcos%5E%7B2%7D+%28x%29+%7D%3D1%5C%5C%5C%5C%5C%5C%0A+%5Cdfrac%7B5cos%28x%29%7D%7Bcos%5E%7B2%7D%28x%29+%7D++-3+%5Cdfrac%7Bsen%5E%7B2%7D%28x%29+%7D%7Bcos%5E%7B2%7D+%28x%29+%7D%3D+%5Cdfrac%7Bcos+%5E%7B2%7D%28x%29+%7D%7Bcos%5E%7B2%7D%28x%29%7D+%5C%5C%5C%5C%5C%5C%5C%0A+%5Cdfrac%7B+%5B5cos%28x%29-3sen%5E%7B2%7Dx-cos%5E%7B2%7Dx%5D%7D%7Bcos%5E%7B2%7D+%28x%29%7D+%5C%5C%5C%5C%5C%5C%5C%0A+%5Cdfrac%7B5cos%28x%29-3%5B1-cos%5E%7B2%7Dx%5D-cos%5E%7B2%7Dx%7D%7B++cos%5E%7B2%7D%28x%29+%7D+%5C%5C%5C%5C%5C%5C%5C%0A++%5Cdfrac%7B5cos%28x%29-3%2B3cos%5E%7B2%7Dx-cos%5E%7B2%7Dx+%7D%7B2cos%5E%7B2%7Dx+%7D%5C%5C%5C%5C%5C%5C%5C%0A+2cos%5E%7B2%7Dx%2B5cos%28x%29%5Cdfrac%7B-3cos%5E%7B2%7Dx+%7D%7Bcos%5E%7B2%7Dx+%7D+%5C%5C%5C%5C%5C%5C%5C%0A2cos%5E%7B2%7Dx%2B5cos%28x%29-3%3D0%5C%5C%5C%5C%0AUma+%7E%7Eequacao%7E%7E+do+%7E%7Esegundo+%7E%7Egrau.%0A+ "5sec(x)-3tan^{2}x=1\\\\\\
5 \dfrac{1}{cos(x)}-3 \dfrac{sen^{2}(x) }{cos^{2} (x) }=1\\\\\\
\dfrac{5cos(x)}{cos^{2}(x) } -3 \dfrac{sen^{2}(x) }{cos^{2} (x) }= \dfrac{cos ^{2}(x) }{cos^{2}(x)} \\\\\\\
\dfrac{ [5cos(x)-3sen^{2}x-cos^{2}x]}{cos^{2} (x)} \\\\\\\
\dfrac{5cos(x)-3[1-cos^{2}x]-cos^{2}x}{ cos^{2}(x) } \\\\\\\
\dfrac{5cos(x)-3+3cos^{2}x-cos^{2}x }{2cos^{2}x }\\\\\\\
2cos^{2}x+5cos(x)\dfrac{-3cos^{2}x }{cos^{2}x } \\\\\\\
2cos^{2}x+5cos(x)-3=0\\\\
Uma ~~equacao~~ do ~~segundo ~~grau.")
![2cos^{2}x+5cos(x)-3=0\\\\
Fazendo \\\\
2t^{2}+5t-3=0\\\\\\
Formula ~~de~~ Baskara.\\\\\\
t= \dfrac{-b\pm \sqrt{b^{2} -4.a.c}}{2.a} \\\\\\\
t= \dfrac{-5\pm \sqrt{5^{2} -4.2.(-3)}}{2.2} \\\\\\\
t= \dfrac{-5\pm \sqrt{25 +24}}{4} \\\\\\\
t= \dfrac{-5\pm \sqrt{49}}{4} \\\\\\\
t= \dfrac{-5\pm 7}{4} \\\\\\\
t_{1} = \dfrac{-5+7}{4}= \dfrac{2}{4}= \dfrac{1}{2}\\\\\\\
t_{2} = \dfrac{-5-7}{4}= \dfrac{-12}{4}= -3\\\\\\\
Nao ~~existe~~ cos~~ de -3](https://tex.z-dn.net/?f=2cos%5E%7B2%7Dx%2B5cos%28x%29-3%3D0%5C%5C%5C%5C%0A%0AFazendo+%5C%5C%5C%5C%0A2t%5E%7B2%7D%2B5t-3%3D0%5C%5C%5C%5C%5C%5C%0AFormula+%7E%7Ede%7E%7E+Baskara.%5C%5C%5C%5C%5C%5C%0At%3D+%5Cdfrac%7B-b%5Cpm+%5Csqrt%7Bb%5E%7B2%7D+-4.a.c%7D%7D%7B2.a%7D+%5C%5C%5C%5C%5C%5C%5C%0At%3D+%5Cdfrac%7B-5%5Cpm+%5Csqrt%7B5%5E%7B2%7D+-4.2.%28-3%29%7D%7D%7B2.2%7D+%5C%5C%5C%5C%5C%5C%5C%0At%3D+%5Cdfrac%7B-5%5Cpm+%5Csqrt%7B25+%2B24%7D%7D%7B4%7D+%5C%5C%5C%5C%5C%5C%5C%0At%3D+%5Cdfrac%7B-5%5Cpm+%5Csqrt%7B49%7D%7D%7B4%7D+%5C%5C%5C%5C%5C%5C%5C%0At%3D+%5Cdfrac%7B-5%5Cpm+7%7D%7B4%7D+%5C%5C%5C%5C%5C%5C%5C%0A+t_%7B1%7D+%3D+%5Cdfrac%7B-5%2B7%7D%7B4%7D%3D+%5Cdfrac%7B2%7D%7B4%7D%3D+%5Cdfrac%7B1%7D%7B2%7D%5C%5C%5C%5C%5C%5C%5C%0At_%7B2%7D+%3D+%5Cdfrac%7B-5-7%7D%7B4%7D%3D+%5Cdfrac%7B-12%7D%7B4%7D%3D+-3%5C%5C%5C%5C%5C%5C%5C%0ANao+%7E%7Eexiste%7E%7E+cos%7E%7E+de+-3%0A "2cos^{2}x+5cos(x)-3=0\\\\
Fazendo \\\\
2t^{2}+5t-3=0\\\\\\
Formula ~~de~~ Baskara.\\\\\\
t= \dfrac{-b\pm \sqrt{b^{2} -4.a.c}}{2.a} \\\\\\\
t= \dfrac{-5\pm \sqrt{5^{2} -4.2.(-3)}}{2.2} \\\\\\\
t= \dfrac{-5\pm \sqrt{25 +24}}{4} \\\\\\\
t= \dfrac{-5\pm \sqrt{49}}{4} \\\\\\\
t= \dfrac{-5\pm 7}{4} \\\\\\\
t_{1} = \dfrac{-5+7}{4}= \dfrac{2}{4}= \dfrac{1}{2}\\\\\\\
t_{2} = \dfrac{-5-7}{4}= \dfrac{-12}{4}= -3\\\\\\\
Nao ~~existe~~ cos~~ de -3")
![Usando~~ a~~ relacao~~fundamental\\\\\\
sen^{2}x+cos^{2}x=1\\\\\\
sen^{2}x+ (\frac{1}{2})^{2}=1 \\\\\\\\\
sen^{2}x+ (\frac{1}{4})=1 \\\\\\
4sen^{2}x+1=4\\\\\\\
4sen^{2}x=4-1\\\\\\\
4sen^{2}x=3\\\\\\\
sen(x)= \frac{\sqrt{3} }{\sqrt{4} }\\\\\\
sen(x)= \frac{\sqrt{3} }{2}](https://tex.z-dn.net/?f=Usando%7E%7E+a%7E%7E+relacao%7E%7Efundamental%5C%5C%5C%5C%5C%5C%0Asen%5E%7B2%7Dx%2Bcos%5E%7B2%7Dx%3D1%5C%5C%5C%5C%5C%5C%0Asen%5E%7B2%7Dx%2B+%28%5Cfrac%7B1%7D%7B2%7D%29%5E%7B2%7D%3D1++%5C%5C%5C%5C%5C%5C%5C%5C%5C%0Asen%5E%7B2%7Dx%2B+%28%5Cfrac%7B1%7D%7B4%7D%29%3D1+%5C%5C%5C%5C%5C%5C%0A4sen%5E%7B2%7Dx%2B1%3D4%5C%5C%5C%5C%5C%5C%5C%0A4sen%5E%7B2%7Dx%3D4-1%5C%5C%5C%5C%5C%5C%5C%0A4sen%5E%7B2%7Dx%3D3%5C%5C%5C%5C%5C%5C%5C%0Asen%28x%29%3D+%5Cfrac%7B%5Csqrt%7B3%7D+%7D%7B%5Csqrt%7B4%7D+%7D%5C%5C%5C%5C%5C%5C%0Asen%28x%29%3D+%5Cfrac%7B%5Csqrt%7B3%7D+%7D%7B2%7D++%0A "Usando~~ a~~ relacao~~fundamental\\\\\\
sen^{2}x+cos^{2}x=1\\\\\\
sen^{2}x+ (\frac{1}{2})^{2}=1 \\\\\\\\\
sen^{2}x+ (\frac{1}{4})=1 \\\\\\
4sen^{2}x+1=4\\\\\\\
4sen^{2}x=4-1\\\\\\\
4sen^{2}x=3\\\\\\\
sen(x)= \frac{\sqrt{3} }{\sqrt{4} }\\\\\\
sen(x)= \frac{\sqrt{3} }{2}")
Exercicio 84
![sen^{2}(x)-5sen(x).cos(x)+cos^{2}(x)=3\\\\\
sen^{2}(x)+cos^{2}(x)-5sen(x).cos(x)=3\\\\\\
relacao~~fundamental\\\\\\ sen^{2}x+cos^{2}x=1\\\\\\\
1-5sen(x).cos(x)=3\\\\\\\\
identidade~~cos(x)tan(x)=sen(x)~~entao.\\\\\\\\
1-5sen(x).cos(x)=3\\\\\\
-5sen(x).cos(x)=3-1\\\\\\
-5sen(x).cos(x)=2\\\\\\
-5tan(x)cos(x).cos(x)=2\\\\\\
Tan(x)= \dfrac{sen(x)}{cos(x)} \\\\\\
-5 \frac{sen(x)}{cos(x)} .cos(x)=2\\\\\\
cos(x)[ \frac{-5sen(x).1}{cos(x)}]=2\\\\\\\](https://tex.z-dn.net/?f=sen%5E%7B2%7D%28x%29-5sen%28x%29.cos%28x%29%2Bcos%5E%7B2%7D%28x%29%3D3%5C%5C%5C%5C%5C%0Asen%5E%7B2%7D%28x%29%2Bcos%5E%7B2%7D%28x%29-5sen%28x%29.cos%28x%29%3D3%5C%5C%5C%5C%5C%5C%0Arelacao%7E%7Efundamental%5C%5C%5C%5C%5C%5C+sen%5E%7B2%7Dx%2Bcos%5E%7B2%7Dx%3D1%5C%5C%5C%5C%5C%5C%5C%0A1-5sen%28x%29.cos%28x%29%3D3%5C%5C%5C%5C%5C%5C%5C%5C%0Aidentidade%7E%7Ecos%28x%29tan%28x%29%3Dsen%28x%29%7E%7Eentao.%5C%5C%5C%5C%5C%5C%5C%5C%0A1-5sen%28x%29.cos%28x%29%3D3%5C%5C%5C%5C%5C%5C%0A-5sen%28x%29.cos%28x%29%3D3-1%5C%5C%5C%5C%5C%5C%0A-5sen%28x%29.cos%28x%29%3D2%5C%5C%5C%5C%5C%5C%0A%0A-5tan%28x%29cos%28x%29.cos%28x%29%3D2%5C%5C%5C%5C%5C%5C%0ATan%28x%29%3D+%5Cdfrac%7Bsen%28x%29%7D%7Bcos%28x%29%7D+%5C%5C%5C%5C%5C%5C%0A-5+%5Cfrac%7Bsen%28x%29%7D%7Bcos%28x%29%7D+.cos%28x%29%3D2%5C%5C%5C%5C%5C%5C%0Acos%28x%29%5B+%5Cfrac%7B-5sen%28x%29.1%7D%7Bcos%28x%29%7D%5D%3D2%5C%5C%5C%5C%5C%5C%5C+%0A%0A%0A%0A "sen^{2}(x)-5sen(x).cos(x)+cos^{2}(x)=3\\\\\
sen^{2}(x)+cos^{2}(x)-5sen(x).cos(x)=3\\\\\\
relacao~~fundamental\\\\\\ sen^{2}x+cos^{2}x=1\\\\\\\
1-5sen(x).cos(x)=3\\\\\\\\
identidade~~cos(x)tan(x)=sen(x)~~entao.\\\\\\\\
1-5sen(x).cos(x)=3\\\\\\
-5sen(x).cos(x)=3-1\\\\\\
-5sen(x).cos(x)=2\\\\\\
-5tan(x)cos(x).cos(x)=2\\\\\\
Tan(x)= \dfrac{sen(x)}{cos(x)} \\\\\\
-5 \frac{sen(x)}{cos(x)} .cos(x)=2\\\\\\
cos(x)[ \frac{-5sen(x).1}{cos(x)}]=2\\\\\\\")
![-5sen(x)=2\\\\\\
sen(x)= \dfrac{2}{5}\\\\\\\
Novamente~~a~~relacao~~fundamental\\\\\\
sen^{2}x+cos^{2}x=1\\\\\\\
( \frac{-2}{5}) ^{2}+cos^{2}x=1\\\\\\\
( \frac{4}{25}) ^{2}+cos^{2}x=1\\\\\\\
4+25cos^{2}x=25\\\\\\
25cos^{2}=25-4\\\\\\
25cos^{2}=21\\\\\\
cos^{2}x= \dfrac{21}{25}\\\\\\
cos(x)= \sqrt{\dfrac{21}{25} }\\\\\\\
cos(x)= \dfrac{ \sqrt{21} }{5}\\\\\\\\\](https://tex.z-dn.net/?f=-5sen%28x%29%3D2%5C%5C%5C%5C%5C%5C%0Asen%28x%29%3D+%5Cdfrac%7B2%7D%7B5%7D%5C%5C%5C%5C%5C%5C%5C%0A%0ANovamente%7E%7Ea%7E%7Erelacao%7E%7Efundamental%5C%5C%5C%5C%5C%5C%0Asen%5E%7B2%7Dx%2Bcos%5E%7B2%7Dx%3D1%5C%5C%5C%5C%5C%5C%5C%0A%28+%5Cfrac%7B-2%7D%7B5%7D%29+%5E%7B2%7D%2Bcos%5E%7B2%7Dx%3D1%5C%5C%5C%5C%5C%5C%5C%0A%28+%5Cfrac%7B4%7D%7B25%7D%29+%5E%7B2%7D%2Bcos%5E%7B2%7Dx%3D1%5C%5C%5C%5C%5C%5C%5C%0A4%2B25cos%5E%7B2%7Dx%3D25%5C%5C%5C%5C%5C%5C%0A25cos%5E%7B2%7D%3D25-4%5C%5C%5C%5C%5C%5C%0A+25cos%5E%7B2%7D%3D21%5C%5C%5C%5C%5C%5C%0Acos%5E%7B2%7Dx%3D+%5Cdfrac%7B21%7D%7B25%7D%5C%5C%5C%5C%5C%5C%0Acos%28x%29%3D+%5Csqrt%7B%5Cdfrac%7B21%7D%7B25%7D+%7D%5C%5C%5C%5C%5C%5C%5C%0Acos%28x%29%3D+%5Cdfrac%7B+%5Csqrt%7B21%7D+%7D%7B5%7D%5C%5C%5C%5C%5C%5C%5C%5C%5C%0A%0A+++ "-5sen(x)=2\\\\\\
sen(x)= \dfrac{2}{5}\\\\\\\
Novamente~~a~~relacao~~fundamental\\\\\\
sen^{2}x+cos^{2}x=1\\\\\\\
( \frac{-2}{5}) ^{2}+cos^{2}x=1\\\\\\\
( \frac{4}{25}) ^{2}+cos^{2}x=1\\\\\\\
4+25cos^{2}x=25\\\\\\
25cos^{2}=25-4\\\\\\
25cos^{2}=21\\\\\\
cos^{2}x= \dfrac{21}{25}\\\\\\
cos(x)= \sqrt{\dfrac{21}{25} }\\\\\\\
cos(x)= \dfrac{ \sqrt{21} }{5}\\\\\\\\\")
![sen(x)= \dfrac{2}{5}\\\\\\\
cos(x)= \dfrac{ \sqrt{21} }{5}\\\\\\\
Tan(x)=\dfrac{sen(x)}{cos(x)}\\\\\\\
Tan(x)=\dfrac{ \dfrac{2}{5} }{ \dfrac{ \sqrt{21}}{5}}\\\\\\\
Tan(x)=\dfrac{2}{5}\times \dfrac{5}{\sqrt{21}} \\\\\\\
Tan(x)=\dfrac{2}{ \sqrt{21} }\\\\\\\
Tan(x)= \frac{2 \sqrt{21} }{21}](https://tex.z-dn.net/?f=sen%28x%29%3D+%5Cdfrac%7B2%7D%7B5%7D%5C%5C%5C%5C%5C%5C%5C%0Acos%28x%29%3D+%5Cdfrac%7B+%5Csqrt%7B21%7D+%7D%7B5%7D%5C%5C%5C%5C%5C%5C%5C%0ATan%28x%29%3D%5Cdfrac%7Bsen%28x%29%7D%7Bcos%28x%29%7D%5C%5C%5C%5C%5C%5C%5C%0ATan%28x%29%3D%5Cdfrac%7B++%5Cdfrac%7B2%7D%7B5%7D+%7D%7B+%5Cdfrac%7B+%5Csqrt%7B21%7D%7D%7B5%7D%7D%5C%5C%5C%5C%5C%5C%5C%0ATan%28x%29%3D%5Cdfrac%7B2%7D%7B5%7D%5Ctimes++%5Cdfrac%7B5%7D%7B%5Csqrt%7B21%7D%7D+%5C%5C%5C%5C%5C%5C%5C%0A%0ATan%28x%29%3D%5Cdfrac%7B2%7D%7B+%5Csqrt%7B21%7D+%7D%5C%5C%5C%5C%5C%5C%5C%0ATan%28x%29%3D+%5Cfrac%7B2+%5Csqrt%7B21%7D+%7D%7B21%7D+ "sen(x)= \dfrac{2}{5}\\\\\\\
cos(x)= \dfrac{ \sqrt{21} }{5}\\\\\\\
Tan(x)=\dfrac{sen(x)}{cos(x)}\\\\\\\
Tan(x)=\dfrac{ \dfrac{2}{5} }{ \dfrac{ \sqrt{21}}{5}}\\\\\\\
Tan(x)=\dfrac{2}{5}\times \dfrac{5}{\sqrt{21}} \\\\\\\
Tan(x)=\dfrac{2}{ \sqrt{21} }\\\\\\\
Tan(x)= \frac{2 \sqrt{21} }{21}")
Boa tarde!
Bons estudos!
Solução!
Exercicio 83
Exercicio 84
Boa tarde!
Bons estudos!
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