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3 years ago

10) Given sin 0 = 0.259 and tan 0 = -0.268,

Mathematics

1 answer:

nikitadnepr [17]3 years ago

6 0

Answer:

(A) cos $\theta$ = -0.9664

$cos \theta =-0.9659$

Step-by-step explanation:

Given

$sin \theta = 0.259 \:and;\\ tan \theta = -0.268$

Sine is Positive and Tangent is Negative in Quadrant II.

In Quadrant II, Cosine is also Negative.

$sin \theta = 0.259 \\\theta=arcsin 0.259=15.01^\circ\\$Therefore in Quadrant II:\\cos \theta =-cos\:15.01^\circ =-0.9659$

Closest Option is A.

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$\bf \begin{array}{lccclll}
&\stackrel{liters}{amount}&\stackrel{alcohol~\%}{quantity}&\stackrel{liters}{alcohol}\\
&------&------&------\\
\textit{18\% solution}&x&0.18&0.18x\\
\textit{40\% solution}&y&0.40&0.4y\\
------&------&------&------\\
mixture&10&0.20&2
\end{array}$

$\bf \begin{cases}
x+y=10\implies \boxed{y}=10-x\\
0.18x+0.4y=2\\
----------\\
0.18x+0.4\left( \boxed{10-x} \right)=2
\end{cases}
\\\\\\
0.18x-0.4x+4=2\implies -0.22x=-2
\\\\\\
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