When the axes are rotated through an angle `60^(0)`
The point R is changed as (2,0). Find R.

Answer

To solve the problem of finding the original coordinates \( R(x, y) \) when the axes are rotated through an angle of \( 60^\circ \) and the new coordinates \( R'(x', y') \) are given as \( (2, 0) \), we can use the formulas for rotation of axes.

### Step-by-Step Solution:

1. **Understand the Rotation Formulas**:
When the axes are rotated by an angle \( \theta \) in the anti-clockwise direction, the transformation from the original coordinates \( (x, y) \) to the new coordinates \( (x', y') \) is given by:
\[ x = x' \cos \theta - y' \sin \theta \]
\[ y = x' \sin \theta + y' \cos \theta \]

2. **Identify the Given Values**:
Here, we have:
- \( x' = 2 \)
- \( y' = 0 \)
- \( \theta = 60^\circ \)

3. **Calculate \( \cos 60^\circ \) and \( \sin 60^\circ \)**:
From trigonometric values:
- \( \cos 60^\circ = \frac{1}{2} \)
- \( \sin 60^\circ = \frac{\sqrt{3}}{2} \)

4. **Substitute Values into the Formulas**:
Using the formulas:
- For \( x \):
\[ x = 2 \cdot \cos 60^\circ - 0 \cdot \sin 60^\circ \]
\[ x = 2 \cdot \frac{1}{2} - 0 = 1 \]

- For \( y \):
\[ y = 2 \cdot \sin 60^\circ + 0 \cdot \cos 60^\circ \]
\[ y = 2 \cdot \frac{\sqrt{3}}{2} + 0 = \sqrt{3} \]

5. **Final Result**:
Therefore, the original point \( R \) is:
\[ R(1, \sqrt{3}) \]

### Summary:
The original coordinates \( R \) before the rotation are \( (1, \sqrt{3}) \).