Explanation:

To understand the relationship between x and y in terms of theta, let's break down the given expressions step by step.

1. Expression for x:
x = 2(theta * sin(theta))

Here, theta is a variable that represents an angle. The expression theta * sin(theta) denotes the product of the angle theta and the sine of theta. The product is then multiplied by 2 to obtain the value of x.

2. Expression for y:
y = 2(1 - cos(theta))

Similarly, in the expression for y, theta is the angle variable. The expression 1 - cos(theta) represents the subtraction of the cosine of theta from 1. The resulting value is then multiplied by 2 to obtain the value of y.

Relationship between x and y:

To establish the relationship between x and y, we can substitute the expression for x into the expression for y:

y = 2(1 - cos(theta))
= 2 - 2cos(theta)

Since x = 2(theta * sin(theta)), we can rewrite it as:

x = 2theta * sin(theta)

Now, let's substitute this expression into the equation for y:

y = 2 - 2cos(theta)
= 2 - 2cos(theta) * (x / 2theta)
= 2 - x * cos(theta) / theta

Hence, we have established the relationship between x and y:

y = 2 - (x * cos(theta)) / theta

Summary:

In summary, the given expressions x = 2(theta * sin(theta)) and y = 2(1 - cos(theta)) represent the values of x and y in terms of the angle theta. By substituting the expression for x into the equation for y, we derive the relationship between x and y as y = 2 - (x * cos(theta)) / theta. This relationship allows us to determine the value of y for a given value of x and theta.