As part of a video game, the point (3, 5) is rotated counterclockwise about the origin through an angle of 25 degrees. Find the new coordinates of this point: x = [__________] y = [__________] Question Help: ▶️ Video [Submit Question] Button --- For educational purposes: To determine the new coordinates after rotation, use the rotation formulas: \[ x' = x \cdot \cos(\theta) - y \cdot \sin(\theta) \] \[ y' = x \cdot \sin(\theta) + y \cdot \cos(\theta) \] Where \((x, y)\) are the original coordinates, \((x', y')\) are the new coordinates, and \(\theta\) is the angle of rotation (in this case, 25 degrees). Make sure to convert the angle to radians if using a calculator that requires it.

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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As part of a video game, the point (3, 5) is rotated counterclockwise about the origin through an angle of 25 degrees.

Find the new coordinates of this point:

x = [__________]

y = [__________]

Question Help: ▶️ Video

[Submit Question] Button

---

For educational purposes:

To determine the new coordinates after rotation, use the rotation formulas:

\[ x' = x \cdot \cos(\theta) - y \cdot \sin(\theta) \]
\[ y' = x \cdot \sin(\theta) + y \cdot \cos(\theta) \]

Where \((x, y)\) are the original coordinates, \((x', y')\) are the new coordinates, and \(\theta\) is the angle of rotation (in this case, 25 degrees). Make sure to convert the angle to radians if using a calculator that requires it.
Transcribed Image Text:As part of a video game, the point (3, 5) is rotated counterclockwise about the origin through an angle of 25 degrees. Find the new coordinates of this point: x = [__________] y = [__________] Question Help: ▶️ Video [Submit Question] Button --- For educational purposes: To determine the new coordinates after rotation, use the rotation formulas: \[ x' = x \cdot \cos(\theta) - y \cdot \sin(\theta) \] \[ y' = x \cdot \sin(\theta) + y \cdot \cos(\theta) \] Where \((x, y)\) are the original coordinates, \((x', y')\) are the new coordinates, and \(\theta\) is the angle of rotation (in this case, 25 degrees). Make sure to convert the angle to radians if using a calculator that requires it.
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