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The Cartesian coordinates of a point are given. (b) (1, -3) (i) Find polar coordinates (r,...

Question:

The Cartesian coordinates of a point are given.

(b) (1, -3)

(i) Find polar coordinates {eq}(r, \theta) {/eq} of the point, where r > 0 and {eq}0 \leq \theta < 2 \pi {/eq}.

(ii) Find polar coordinates {eq}(r, \theta) {/eq} of the point, where r < 0 and {eq}0 \leq \theta < 2 \pi {/eq}.

NOTE: It does not accept the answer as a function of arctangent.

Conversion from Cartesian Coordinates to Polar Coordinates:

If a point in Cartesian coordinate is {eq}(x,y) {/eq} then its polar coordinate is {eq}(r, \theta ) {/eq}

Where:

{eq}r = \pm \sqrt{x^{2}+y^{2}} \, \, and \, \, \theta = \tan^{-1} \mid \frac{y}{x} \mid {/eq}

{eq}r {/eq} is the distance from origin to the point and {eq}\theta {/eq} is an angle between the line which is from origin to the point and the {eq}x- {/eq}axis in polar coordinates.

Answer and Explanation: 1

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i.)

We are given:

{eq}(x,y) = (1, -3 ) {/eq}

Now:

{eq}r = \pm \sqrt{ (1)^2 + (-3)^{2} } = \pm \sqrt{10} {/eq}

{eq}\theta = \tan^{-1} \mid...

See full answer below.


Learn more about this topic:

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The Cartesian Coordinate System: Plotting Points & Graphing Lines

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Chapter 12 / Lesson 2
31K

What is the Cartesian coordinate system? Learn how to locate points on the Cartesian plane and see examples of how the system is used to graph lines.


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