Question

The amplitude of a trigonometric function is equal to __________ the coefficient of the trigonometric term.

A) Half
B) Double
C) Square root of
D) Reciprocal of

Answer 1

The amplitude of a trigonometric function is equal to the absolute value of its coefficient, which is the number in front of the sine or cosine term representing the function's maximum displacement from the center line. The correct option is not mentioned in the options.

Step-by-step explanation:

The amplitude of a trigonometric function is equal to the coefficient of the trigonometric term. Therefore, correct answer to the fill-in-the-blank question is that the amplitude of a trigonometric function is equal to the absolute value of the coefficient of the trigonometric term in the function.

For example, in the trigonometric function f(x) = A sin(Bx + C) or f(x) = A cos(Bx + C), the coefficient A determines the amplitude of the wave. The absolute value is used because amplitude is always a positive quantity, indicating the maximum displacement from the center line or equilibrium position.