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fenix001 [56]
2 years ago
9

Evaluate the cosine if the angle of rotation which contains the point (9, -3) on its terminal side

Mathematics
1 answer:
Liono4ka [1.6K]2 years ago
6 0

so we know the terminal point is at (9, -3), now, let's notice that's the IV Quadrant

\bf (\stackrel{x}{9}~~,~~\stackrel{y}{-3})\impliedby \textit{let's find the \underline{hypotenuse}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c=\sqrt{a^2+b^2} \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ c=\sqrt{9^2+(-3)^2}\implies c=\sqrt{81+9}\implies c=\sqrt{90} \\\\[-0.35em] ~\dotfill

\bf cos(\theta )=\cfrac{\stackrel{adjacent}{9}}{\stackrel{hypotenuse}{\sqrt{90}}}\implies \stackrel{\textit{rationalizing the denominator}}{\cfrac{9}{\sqrt{90}}\cdot \cfrac{\sqrt{90}}{\sqrt{90}}\implies \cfrac{9\sqrt{90}}{90}}\implies \cfrac{\sqrt{90}}{10}\implies \cfrac{3\sqrt{10}}{10}

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Answer:

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Step-by-step explanation:

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Slope of given line= -\frac{3}{4}

Parallel lines have the same slope. Thus, the slope of the line would also be -\frac{3}{4}.

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The value of c can be found by substituting a pair of coordinates.

When x= 4, y= -1,

-1=-\frac{3}{4} (4)+c

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<em>Add 3 to both sides:</em>

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Additional:

Do check out the following for a similar question on slope-intercept form!

  • brainly.com/question/25549430
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