'Simplified Cartesian to Polar Conversion with an Applied Example'

Title: "Simplified Cartesian to Polar Conversion with an Applied Example"

(The Circle 11.11 Series)
#nolieism

Introduction: Converting Cartesian coordinates to polar coordinates is a fundamental mathematical transformation, useful in various fields, including physics and engineering. This discussion will present a simplified formula approach and provide an applied example to illustrate its practical use.

Cartesian to Polar Conversion Formula: The conversion from Cartesian coordinates (x, y) to polar coordinates (r, θ) can be achieved using the following formulas:

r (radius): r = √(x^2 + y^2)

θ (angle): θ = arctan(y / x)

Applied Example: Let's say we have a point in the Cartesian plane with coordinates (3, 4). We want to convert these coordinates to polar form.

Step 1 - Calculate r (radius): r = √(3^2 + 4^2) = √(9 + 16) = √25 = 5

Step 2 - Calculate θ (angle): θ = arctan(4 / 3)

Using a calculator, we find θ ≈ 53.13 degrees (rounded to two decimal places).

So, the polar coordinates of the point (3, 4) are (5, 53.13°).

Conclusion: The simplified Cartesian to Polar Conversion allows us to transform coordinates from the Cartesian plane to the polar plane using straightforward mathematical formulas. This conversion is valuable in many real-world applications, providing a better understanding of spatial relationships and facilitating calculations involving angles and distances.

#By Sir NolieBoy Rama Bantanos
(The Circle 11.11 Series)