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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View this answeri.)
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...
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Learn more about this topic:
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Chapter 12 / Lesson 2What 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.