Mathematics: Exactly find sin(x+y) if sinx= 1/3 where x ends in the 2ndquadrant and cosy= 1/5 where y ends in the first quadrant.

Exactly find sin(x+y) if sinx= 1/3 where x ends in

Ответ:

Domi0129

02.01.2022

Mathematics

$\sin(x+y)=\dfrac{1-8\sqrt{3}}{15}$

Step-by-step explanation:

Since we have given that

$\sin x=\dfrac{1}{3}\\\\so,\\\\\cos x=\sqrt{1-\dfrac{1}{9}}=\sqrt{\dfrac{8}{9}}=\dfrac{2\sqrt{2}}{3}$

Since x ends in the 2 nd quadrant,

So, $\cos x=\dfrac{-2\sqrt{2}}{3}$

Similarly,

$\cos y=\dfrac{1}{5}\\\\So,\\\\\sin y=\sqrt{1-\dfrac{1}{25}}=\sqrt{\dfrac{24}{25}}=\dfrac{2\sqrt{6}}{5}$

So, sin(x+y) is given by

$\sin x\cos y+\sin y\cos x\\\\\\=\dfrac{1}{3}\times \dfrac{1}{5}+\dfrac{2\sqrt{6}}{5}\times (-)\dfrac{2\sqrt{2}}{3}\\\\\\=\dfrac{1}{15}-\dfrac{8\sqrt{3}}{15}\\\\\\=\dfrac{1-8\sqrt{3}}{15}$

Hence, $\sin(x+y)=\dfrac{1-8\sqrt{3}}{15}$

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Ответ:

orangeicecream

11.09.2022

Mathematics

That would be $705.01

Step-by-step explanation:

Hope this helped

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Exactly find sin(x+y) if sinx= 1/3 where x ends in the
2ndquadrant and cosy= 1/5 where y ends in the first quadrant.

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