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Let u and v be angles in the first quadrant, and let sinu=1/3 and sinv=1/4. Then cos⁡u = , cos⁡v = ,sin⁡(u+v) = .

Respuesta :

LammettHash
Recall that [tex]\sin^2x+\cos^2x=1[/tex].

This means

[tex]\cos u=\sqrt{1-\sin^2u}=\sqrt{1-\dfrac19}=\dfrac{\sqrt8}3=\dfrac{2\sqrt2}3[/tex]
[tex]cos v=sqrt{1-\sin^2v}=\sqrt{1-\dfrac1{16}}=\dfrac{\sqrt{15}}4[/tex]
[tex]\sin(u+v)=\sin u\cos v+\sin v\cos u=\dfrac13\times\dfrac{\sqrt{15}}4+\dfrac14\times\dfrac{2\sqrt2}3=\dfrac{2\sqrt2+\sqrt{15}}{12}[/tex]

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