# Rotation Calculator

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## What is Rotation Calculator?

A Rotation Calculator is a tool that can be used to calculate the new coordinates of a point after rotating it by a given angle. This is useful in various fields such as mathematics, physics, engineering, and computer graphics. In this article, we will discuss the formula used to calculate the new coordinates, how to use the calculator, and answer some frequently asked questions.

### Formula:

The formula used to calculate the new coordinates of a point (x,y) after rotating it by an angle θ in radians is:

newX = x * cos(θ) – y * sin(θ) newY = x * sin(θ) + y * cos(θ)

The above formula applies a clockwise rotation. To apply an anti-clockwise rotation, the signs of the sin terms are reversed:

newX = x * cos(θ) + y * sin(θ) newY = -x * sin(θ) + y * cos(θ)

### Example:

Suppose we have a point (3,4) and we want to rotate it by an angle of 45 degrees anti-clockwise. To calculate the new coordinates, we can use the formula as follows:

θ = 45 degrees * π / 180 = 0.7854 radians x = 3, y = 4 newX = 3 * cos(0.7854) + 4 * sin(0.7854) = 0.35 + 4.35 = 4.70 newY = -3 * sin(0.7854) + 4 * cos(0.7854) = -2.93 + 2.83 = -0.10

Therefore, the new coordinates of the point after rotation are approximately (4.70,-0.10).

### How to use the Rotation Calculator:

To use the Rotation Calculator, follow these steps:

- Enter the X-coordinate and Y-coordinate of the point you want to rotate.
- Enter the Angle of Rotation in degrees or radians, depending on your choice.
- Choose the Units of Angle (Degrees or Radians).
- Choose the Rotation direction (Clockwise or Anti-clockwise).
- Click the Calculate button.
- The new X-coordinate and Y-coordinate will be displayed.

### FAQs:

**What is the difference between clockwise and anti-clockwise rotation?**

Clockwise rotation is when a point is rotated in the direction of a clock’s hands. Anti-clockwise rotation is when a point is rotated in the opposite direction.

**What are the units of angle used in the Rotation Calculator?**

The units of angle used in the Rotation Calculator are degrees and radians.

**Can I use the Rotation Calculator to rotate multiple points at once?**

No, the Rotation Calculator can only be used to rotate one point at a time. If you have multiple points to rotate, you will need to perform the calculation for each point separately.