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\( \left. \begin{array} { l } { X + S \times \cos ( \frac { \pi \times \theta } { 180 } ) } \\ { Y + S \times \sin ( \frac { \pi \times \theta } { 180 } ) } \end{array} \right. \)

Ask by Simpson Nunez. in Netherlands
Mar 15,2025

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The new coordinates after moving \( S \) units at an angle \( \theta \) from the original point \((X, Y)\) are: \[ \begin{cases} X_{\text{new}} = X + S \times \cos\left(\frac{\pi \times \theta}{180}\right) \\ Y_{\text{new}} = Y + S \times \sin\left(\frac{\pi \times \theta}{180}\right) \end{cases} \]

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Bonus Knowledge

The equation you provided seems to represent the conversion of polar coordinates into Cartesian coordinates. When you have a point defined by a distance \( S \) from the origin and an angle \( \theta \), you can find its x and y components using these trigonometric functions. It’s like plotting a point on a map using direction and distance! In real-world applications, this formula is handy in navigation and robotics, where you often need to determine a position based on an angle and distance from a reference point. For example, if a robot moves a certain distance at a specific angle, you can find its new position using this method, making it crucial for pathfinding and movement strategies!

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