Question

How can amplitude be negative?

Answer 1

Hint: Here, we will use the concept of amplitude and its properties. Amplitude is the distance measured from the center to the maximum point in a graph of trigonometric functions such as sine and cosine functions.

Complete step by step solution:
In the trigonometric branch of mathematics, the amplitude of a trigonometric function is the amount by which the graph of the function travels above and below its midline.
In other words, the amplitude is half the distance from the highest point of the curve to the bottom point of the curve.
Hence, we can write this mathematically as:
Amplitude \[ = \] (Maximum \[ - \] Minimum) \[ \div 2\]
Now, since, the amplitude is a measure of distance, thus, it can never be negative due to the fact that distance is always positive.
Amplitude can have different values but it can never be less than 0.
Thus, the amplitude can never be negative.

Note:
We should keep in mind that sometimes we multiply a trigonometric function by a negative number. This negative number does not make the amplitude negative due to the same fact mentioned above that amplitude is a measure of distance and distance can’t be negative. Thus, for example, if we walk 5 meters backward then we do not write it as \[ - 5\] meters because even if we are moving backward, the area of concern is that the distance covered by us is 5 meters. Thus, this is a perfect example to understand that amplitude can never be negative due to the same reason.