Final answer:
The Cartesian equation representing the curve for the given parametric equations is essentially the identity 1 = 1, after applying the trigonometric Pythagorean identity.
Step-by-step explanation:
To eliminate the parameter in the given equations x = sin(1/2) and y = cos(1/2) and find a Cartesian equation for the curve, we can use the Pythagorean identity which states that sin²(\theta) + cos²(\theta) = 1. Applying this identity, we have:
x² + y² = sin²(1/2) + cos²(1/2).
Replacing x and y with their respective trigonometric forms, we get:
sin²(1/2) + cos²(1/2) = 1.
This simplifies to:
1 = 1,
which is always true for all values of x and y within the given domain (-1 ≤ x ≤ 1). Thus, the curve represented by the parametric equations is the portion of the unit circle for \theta = 1/2 radians.