The greater value of the function `-5 sin theta +12 cos theta` is

Options

A. P
B. V
C. `PV^(2)`
D. RT

Explanation

To find the greater value of the function \( -5 \sin \theta + 12 \cos \theta \), we can use the formula for the maximum value of a function of the form \( a \sin \theta + b \cos \theta \).

### Step-by-step Solution:

1. **Identify the coefficients**:
In the function \( -5 \sin \theta + 12 \cos \theta \), we identify \( a = -5 \) and \( b = 12 \).

2. **Use the maximum value formula**:
The maximum value of the function \( a \sin \theta + b \cos \theta \) is given by the formula:
\[ \text{Max value} = \sqrt{a^2 + b^2} \]

3. **Calculate \( a^2 \) and \( b^2 \)**:
\[ a^2 = (-5)^2 = 25 \]
\[ b^2 = (12)^2 = 144 \]

4. **Sum \( a^2 \) and \( b^2 \)**:
\[ a^2 + b^2 = 25 + 144 = 169 \]

5. **Take the square root**:
\[ \sqrt{a^2 + b^2} = \sqrt{169} = 13 \]

6. **Conclusion**:
The greater value of the function \( -5 \sin \theta + 12 \cos \theta \) is \( 13 \).