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Tresset [83]
3 years ago
5

Please help me. I need help

Mathematics
2 answers:
lesya692 [45]3 years ago
6 0

Look at the first picture.

In Quadrant II tangent is negative and cosine is negative too.

We have:

\tan\theta=-\dfrac{2}{3}=\dfrac{2}{-3}

therefore we have the point (-3, 2) → x = -3 and y = 2.

Calculate r:

r=\sqrt{(-3)^2+2^2}=\sqrt{9+4}=\sqrt{13}

Calculate cosine:

\cos\theta=\dfrac{x}{r}\to\cos\theta=\dfrac{-3}{\sqrt{13}}\\\\\cos\theta=-\dfrac{3}{\sqrt{13}}\cdot\dfrac{\sqrt{13}}{\sqrt{13}}\\\\\cos\theta=-\dfrac{3\sqrt{13}}{13}

Your answer is \boxed{a.\ -\dfrac{3\sqrt{13}}{13}}

mel-nik [20]3 years ago
3 0
<h3>Answer:</h3>

  a.  -(3√13)/13

<h3>Step-by-step explanation:</h3>

The cosine can be found from the tangent by way of the secant.

  tan(θ)² +1 = sec(θ)² = 1/cos(θ)²

Then ...

  cos(θ) = ±1/√(tan(θ)² +1)

The <em>cosine is negative in the second quadrant</em>, so we will choose that sign.

  cos(θ) = -1/√((-2/3)² +1) = -1/√(4/9 +1) = -1/√(13/9)

  cos(θ) = -3/√13 = -(3√13)/13 . . . . . matches your selection A

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