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sin u = -4/5 , pi < u < 3pi/2

 

answers

sin2u = 24/25

cos2u = -17/25 

tan 2u = 4sqrt21/ 17

 

how to do??

Guest May 17, 2017
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avatar+7167 
0

sin u = -4/5 , pi < u < 3pi/2

 

answers

sin2u = 24/25

cos2u = -17/25  not correct

tan 2u = 4sqrt21/ 17

 

how to do?

 

\(sin \ 2u=2sin \ u \cdot cos \ u\\cos \ u=\sqrt{1-sin^2u}\\sin\ 2u=2sin\ u\cdot\sqrt{1-sin^2u}\)

\(sin \ 2u=-\frac{8}{5}\cdot\sqrt{1-\frac{16}{25}}=-\frac{8}{5}\cdot -\sqrt{\frac{9}{25}}=-\frac{8}{5}\cdot -\frac{3}{5}\)

 

\( sin\ 2u=\frac{24}{25}\) 

 

\(cos \ 2u=1-2sin^2u=1-2\cdot\frac{16}{25}\)

 

\(cos\ 2u=-\frac{7}{25}\)

 

\(tan \ 2u=\ \frac{2\cdot tan\ u}{1-tan^2u}\\tan\ u=\pm\ \frac{sin\ u}{\sqrt{1-sin^2u}}\)

\(tan^2u=\frac{sin^2u}{1-sin^2u}=\frac{\frac{16}{25}}{1-\frac{16}{25}}=\frac{16\cdot 25}{25\cdot 9}\)

\(tan\ u =\frac{4}{3}\)

\(tan\ 2u=\frac{\frac{8}{3}}{1-\frac{16}{9}}=-\ \frac{8\cdot 9 }{3\cdot 7}\)

 

\(tan\ 2u=-\ \frac{24}{7}\)

 

laugh  !

asinus  May 17, 2017

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