What is the maximum value of the function f(x) = 3 sin(x) + 4 cos(x)?

5

Expressions of the form A sin(x) + B cos(x) can be rewritten as R sin(x + φ), where R is the square root of (A² + B²). For coefficients 3 and 4, the amplitude is √(3² + 4²) = 5.