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2 years ago

Use the law of wines to find the value of y. Round to the nearest Tenth

Mathematics

1 answer:

Eva8 [605]2 years ago

4 0

Answer:

y ≈ 2.5

Step-by-step explanation:

Using the Sine rule in Δ XYZ

$\frac{sinZ}{XY}$ = $\frac{sinY}{XZ}$ , substitute values

$\frac{sin50}{2}$ = $\frac{sin75}{y}$ ( cross- multiply )

y sin50° = 2 sin75° ( divide both sides by sin50° )

y = $\frac{2sin75}{sin50}$ ≈ 2.5 ( to the nearest tenth )

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Convert: 6y + y² = x² from rectangular to polar form.

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$\bf \textit{Double Angle Identities}
\\ \quad \\
sin(2\theta)=2sin(\theta)cos(\theta)
\\ \quad \\\\
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\begin{cases}
\boxed{cos^2(\theta)-sin^2(\theta)}\\
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2cos^2(\theta)-1
\end{cases}\\\\\\
tan(2\theta)=\cfrac{2tan(\theta)}{1-tan^2(\theta)}\\\\
-------------------------------\\\\$

$\bf 6y+y^2=x^2\implies \cfrac{6y}{x^2}+\cfrac{y^2}{x^2}=1\implies \cfrac{6rsin(\theta )}{[rcos(\theta )]^2}+\cfrac{[rsin(\theta )]^2}{[rcos(\theta )]^2}=1
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$\bf \cfrac{6sin(\theta )}{rcos^2(\theta )}=1-\cfrac{sin^2(\theta )}{cos^2(\theta )}\implies \cfrac{6sin(\theta )}{1-\frac{sin^2(\theta )}{cos^2(\theta )}}=rcos^2(\theta )
\\\\\\
\cfrac{6sin(\theta )}{cos^2(\theta )\left[ 1-\frac{sin^2(\theta )}{cos^2(\theta )} \right]}=r\implies \cfrac{6sin(\theta )}{cos^2(\theta )-sin^2(\theta )}=r
\\\\\\
\cfrac{6sin(\theta )}{cos(2\theta )}=r$

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