Final answer:
The amplitude of the function y = -6cos5x is 6. Therefore, the correct answer is: (b) 6
Step-by-step explanation:
The amplitude of the function y = -6cos5x is 6. The amplitude of a cosine function is the absolute value of the coefficient of the cosine term. In this case, the coefficient is -6, so the amplitude is 6.
To find the amplitude of the function y = -6cos(5x), let's first understand what an amplitude is in the context of a trigonometric function like a cosine.
The amplitude of a trigonometric function is a measure of its maximum displacement from its central position, which is typically its rest or equilibrium position. In simpler terms, it indicates how high or how low the function's graph will go. For the cosine function, this is the maximum value the cosine wave reaches above or below the midline or horizontal axis.
The general form of a cosine function is: y = A*cos(Bx + C) + D Here, A is the amplitude of the cosine wave. It determines the "height" of the wave. Note that the amplitude is always a positive quantity, irrespective of the sign of A in the equation.
The amplitude represents a distance, which cannot be negative. Therefore, even if A is given as a negative value, the amplitude itself is the absolute value of A.
So for the function y = -6cos(5x), the coefficient in front of the cosine function is -6. The amplitude is the absolute value of this coefficient. Thus, the amplitude of y = -6cos(5x) is the absolute value of -6, which is 6. Therefore, the correct answer is: (b) 6