What is the <strong>MAXIMUM</strong> value of a \cos x+b \sin x+c?
- A. \sqrt{a^{2}+b^{2}+c}
- B. \sqrt{a^{2}+b^{2}}+c ✓
- C. \sqrt{a^{2}+b^{2}}-c
- D. \sqrt{a^{2}+b^{2}}
Correct Answer: B. \sqrt{a^{2}+b^{2}}+c
Explanation
The expression a \cos x + b \sin x can be rewritten as R \cos(x - \alpha), where R = \sqrt{a^2+b^2}. Its maximum value is simply \sqrt{a^2+b^2}. Adding the constant c to the expression shifts the maximum value to \sqrt{a^2+b^2} + c.