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Coordinate Rotation Calculator

Formula

To calculate the new coordinates after rotation:

$X = x \cos(\theta) + y \sin(\theta)$

$Y = -x \sin(\theta) + y \cos(\theta)$

What is Coordinate Rotation?

Coordinate rotation involves rotating a point in the x-y plane by a specified angle about the origin. This is commonly used in various fields such as computer graphics, robotics, and physics to transform coordinates and analyze motion or orientation.

Example Calculation 1

Let's assume the following values:

Original X Coordinate $x$ = 3
Original Y Coordinate $y$ = 4
Angle of Rotation $\theta$ = 45 degrees

Step 1: Convert the angle to radians:

$\theta = 45 \times \frac{\pi}{180} = 0.7854 \text{ radians}$

Step 2: Calculate the new X coordinate:

$X = 3 \cos(0.7854) + 4 \sin(0.7854) = 4.95$

Step 3: Calculate the new Y coordinate:

$Y = -3 \sin(0.7854) + 4 \cos(0.7854) = 0.71$

Example Calculation 2

Let's assume the following values:

Original X Coordinate $x$ = 5
Original Y Coordinate $y$ = 6
Angle of Rotation $\theta$ = 90 degrees

Step 1: Convert the angle to radians:

$\theta = 90 \times \frac{\pi}{180} = 1.5708 \text{ radians}$

Step 2: Calculate the new X coordinate:

$X = 5 \cos(1.5708) + 6 \sin(1.5708) = 6$

Step 3: Calculate the new Y coordinate:

$Y = -5 \sin(1.5708) + 6 \cos(1.5708) = -5$