Question

How does amplitude relate to the unit circle?

Answer 1

Hint: Here, we will first find the level of axis of the wheel. Then by using the level of axis and the amplitude formula, we will find the amplitude. We will use the amplitude, to find the relation between the amplitude and the unit circle.

Formula Used: Amplitude of a circle is given by half the diameter of the circle i.e., \[A = \dfrac{d}{2}\]

Complete step by step solution:
We know that if we make the circle larger, then there is a large difference between the all the way up which is also the top most point of the circle and all the way down which is also the lowest point of the circle.
Now, Consider a Ferris wheel. In a Ferris wheel, we know that the level of the axis of the wheel is called \[0\].
We are given with a unit circle.

So, In a unit circle, the maximum height above the level of the axis of the circle \[0\] is \[1\] and the minimum height below the level of the axis of the circle \[0\] is \[1\].
Now, we will find the amplitude of a circle.
We know that amplitude of a circle is given by half the diameter of the circle i.e., \[A = \dfrac{d}{2}\].
Substituting \[a = 2\] in the amplitude formula, we get
\[A = \dfrac{2}{2}\]
\[ \Rightarrow A = 1\]

Therefore, the amplitude of a unit circle is \[1\] which is half the diameter or the radius of the unit circle.

Note:
We know that the amplitude is defined as the height from the center line to the highest point or to the lowest point. We should always remember that amplitude is the radius of the circle and is represented in meters. Also, the Ferris wheel is a non-building structure consisting of a rotating upright wheel with passenger cars attached to the rim in an amusement park. We should always remember that amplitude, period and frequency are only based on the unit circle.