SmailMapsYouTubeTranslateMicrosoft Office Ho...Check You: Paper f...Solve inequalities w..."Use 0 = tanKatarina is correct. Note that Dacia must use the signs of x and y to find on which quadrant the point lies.Part 9 of 10 -AnalyzeThe friends are ready to try a few problems.The Cartesian coordinates of a point in the xy plane are (-3.4, -2.3). Find the polar coordinates of the point.r = 4,10o counterclockwise from the +x-axisSubmitSkip (you cannot come back)Need Help?Read It/1 Points]DETAILS A webassign.net/web/Student/Assignment-Responses/submit?dep=263123668tags=autosave#question4036946 0M GmailMapsYouTubeTranslate O Microsoft Office Ho...Check You: Paper f.Solve inequalities w.They can click and drag the black point at the outer end of the brown line to various points in the xy plane andsee how its Cartesian and polar coordinates change in the readouts at the bottom. Note that 0 is defined asthe angle measured in a direction counterclockwise from the positive x-axis.y (m)x (m)y =|-2,50| m-3.50 | msin e--0.584.30 mcos e =-0.81216 degreestan e-0.71Click bere to onen the simulation in a new windowhp

Answered: The Cartesian coordinates of a point in…

The Cartesian coordinates of a point in the xy plane are (-3.4, -2.3). Find the polar coordinates of the point. r = 410 e = o counterclockwise from the +x-axis

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Microsoft Office Ho...
Check You: Paper f...
Solve inequalities w...
"Use 0 = tan
Katarina is correct. Note that Dacia must use the signs of x and y to find on which quadrant the point lies.
Part 9 of 10 -Analyze
The friends are ready to try a few problems.
The Cartesian coordinates of a point in the xy plane are (-3.4, -2.3). Find the polar coordinates of the point.
r = 4,10
o counterclockwise from the +x-axis
Submit
Skip (you cannot come back)
Need Help?
Read It
/1 Points]
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Expert Solution

Step 1

Plane Polar Coordinates

In-plane polar coordinate system, the position of a point in space is represented by the length of the vector joining the origin with the point and the angle the vector makes with the X axis.

Let $P$ be the point in space. The position of P is represented by the coordinates $(r, θ)$ . The x and y coordinates of the point is represented as

$x = r \cos θ y = r \sin θ$

Thus squaring and adding we get

$x^{2} + y^{2} = {(r \cos θ)}^{2} + {(r \sin θ)}^{2} \Rightarrow r^{2} (\sin^{2} θ + \cos^{2} θ) = x^{2} + y^{2} \Rightarrow r = \sqrt{x^{2} + y^{2}}$

Dividing the two equations we get

$\tan θ = \frac{y}{x} \Rightarrow θ = \tan^{- 1} (\frac{y}{x})$

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