Rotation Calculator (new coordinates by rotation)

To determine the new coordinates after rotating a point around the origin, apply the rotation formulas using the angle of rotation, θ This process adjusts each coordinate based on trigonometric functions for precise new positions.

In geometry, rotation of coordinates is a transformational method that repositions points or shapes around a fixed center. This rotation calculator is really useful for speedily finding the new coordinates after rotating a point by a specific angle around the origin.

Generally, this tool has various applications in mathematics, physics, engineering, and computer graphics. To say the least, this tool is ideal for tasks that involve object rotation, angular adjustments, and transformations in different coordinate systems.

Formula:

Contents

1 Formula:
2 Solved Calculations:
3 What is a Rotation Calculator?
4 Final Words:

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

Variable	Description
$X$	New x-coordinate after rotation
$Y$	New y-coordinate after rotation
$x$	Original x-coordinate
$y$	Original y-coordinate
$\theta$	Angle of rotation (in degrees)

Solved Calculations:

Example 1:

Step	Calculation
Original Point (x, y)	(3, 4)
Angle of Rotation ( $\theta$ )	90°
New X Calculation	$3 \cos(90°) + 4 \sin(90°)$
Result for X	$0 + 4 = 4$
New Y Calculation	$-3 \sin(90°) + 4 \cos(90°)$
Result for Y	$-3 + 0 = -3$

Answer: The new coordinates are (4, -3).

Example 2:

Step	Calculation
Original Point (x, y)	(5, 2)
Angle of Rotation ( $\theta$ )	180°
New X Calculation	$5 \cos(180°) + 2 \sin(180°)$
Result for X	$-5 + 0 = -5$
New Y Calculation	$-5 \sin(180°) + 2 \cos(180°)$
Result for Y	$0 – 2 = -2$

Answer: The new coordinates are (-5, -2).

What is a Rotation Calculator?

The Rotation Calculator (new coordinates by rotation) is a highly invaluable tool for fetching location coordinates. It can locate the new positions of points after rotation around a specified center, usually the origin, by a given angle.

Final Words:

In summing up the things, a rotation calculator simplifies finding new coordinates after rotation by efficiently handling transformations. It’s essential for anyone working with coordinate-based geometry or graphical rotations.