Rotasi Hal 34-36 Bab 1 TRANSFORMASI FUNGSI Kelas 12 SMA SMK Kurikulum Merdeka

Introduction

This tutorial covers the concept of rotation in the context of function transformations, specifically for students in Class 12 under the Kurikulum Merdeka. Understanding rotation is essential for mastering geometric transformations in mathematics. This guide will provide clear, actionable steps to help you grasp the principles and applications of rotation in functions.

Step 1: Understanding Rotation of Functions

• Rotation involves turning a graph around a specific point, typically the origin (0,0).
• The angle of rotation is usually measured in degrees (or radians).
• To rotate a point (x, y) by an angle θ, use the following formulas:
  • New x-coordinate: x' = x * cos(θ) - y * sin(θ)
  • New y-coordinate: y' = x * sin(θ) + y * cos(θ)

Practical Tip

• Familiarize yourself with trigonometric functions (sine and cosine) as they are crucial for performing rotations.

Step 2: Performing a Rotation

1. Identify the point (x, y) that you want to rotate.
2. Determine the angle of rotation (θ).
3. Apply the rotation formulas to calculate the new coordinates (x', y'):
   • Substitute the original coordinates and the angle into the rotation formulas.
4. Plot the new point on the graph.

Common Pitfall

• Be mindful of the angle's direction: positive angles indicate counterclockwise rotation, while negative angles indicate clockwise rotation.

Step 3: Rotating Shapes

• To rotate a shape, apply the rotation formulas to each vertex of the shape.
• Connect the new vertices to form the rotated shape.

Example

• If you have a triangle with vertices A(1, 2), B(3, 4), and C(5, 1) and you want to rotate it 90 degrees counterclockwise:
  1. Rotate point A:
     • A'(0, 1)
  2. Rotate point B:
     • B'(-2, 3)
  3. Rotate point C:
     • C'(-1, 5)

Step 4: Analyzing the Effects of Rotation

• Observe how the position and orientation of the shape change after rotation.
• Understand that the distance from the origin remains constant in a perfect rotation, but the coordinates may change significantly.

Conclusion

In this tutorial, you have learned how to perform rotations on points and shapes within a coordinate system. Remember to practice applying the rotation formulas and plotting the results for better comprehension. As a next step, consider exploring other transformations such as translation, reflection, and dilation, and how they can be combined with rotation for more complex transformations.