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3 years ago

Foci of ellipse of 3x2 + y2 =9

Mathematics

1 answer:

Oksi-84 [34.3K]3 years ago

8 0

Answer:

x=√-1/3 y^2 +3 or x=-√-1/3 y^2 +3

Step-by-step explanation:

Let's solve for x.

3x2+y2=9

Step 1: Add -y^2 to both sides.

3x2+y2+−y2=9+−y2

3x2=−y2+9

Step 2: Divide both sides by 3.

3x^2/3= -y^2+9/3

x^2=-1/3 y^2 +3

x=√-1/3 y^2 +3 or x=-√-1/3 y^2 +3

Hope it helped!

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2 years ago

Considering only the values of β for which sinβtanβsecβcotβ is defined, which of the following expressions is equivalent to sinβ

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Answer:

$\tan(\beta)$

Step-by-step explanation:

For many of these identities, it is helpful to convert everything to sine and cosine, see what cancels, and then work to build out to something. If you have options that you're building toward, aim toward one of them.

${\tan(\theta)}={\dfrac{\sin(\theta)}{\cos(\theta)}$ and ${\sec(\theta)}={\dfrac{1}{\cos(\theta)}$

Recall the following reciprocal identity:

$\cot(\theta)=\dfrac{1}{\tan(\theta)}=\dfrac{1}{ \left ( \dfrac{\sin(\theta)}{\cos(\theta)} \right )} =\dfrac{\cos(\theta)}{\sin(\theta)}$

So, the original expression can be written in terms of only sines and cosines:

$\sin(\beta)\tan(\beta)\sec(\beta)\cot(\beta)$

$\sin(\beta) * \dfrac{\sin(\beta) }{\cos(\beta) } * \dfrac{1 }{\cos(\beta) } * \dfrac{\cos(\beta) } {\sin(\beta) }$

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Working toward one of the answers provided, this is the tangent function.

The one caveat is that the original expression also was undefined for values of beta that caused the sine function to be zero, whereas this simplified function is only undefined for values of beta where the cosine is equal to zero. However, the questions states that we are only considering values for which the original expression is defined, so, excluding those values of beta, the original expression is equivalent to $\tan(\beta)$ .

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2 years ago

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Since sine is negative, so is cosecant as this is the reciprocal of sine

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