Question

Parameterize (write parametric equations for) the Cartesian equation by setting x(t) = t or by setting y(t) = t. y(x) = 8 sin(x) + 5 {X(t), y(t)} = {

Answer 1

To parameterize the given equation y(x) = 8 sin(x) + 5, we set x(t) = t and then substitute t into the equation to obtain y(t) = 8 sin(t) + 5. The resulting parametric equations are x(t) = t and y(t) = 8 sin(t) + 5.

Step-by-step explanation:

To parameterize the Cartesian equation y(x) = 8 sin(x) + 5 where {X(t), y(t)} is the set of parametric equations, we will set x(t) = t to find the corresponding function for y(t). Since we are given the relationship directly as y in terms of x, we can substitute t for x directly into the equation to get the parametric equation for y(t).

Following our substitution, we get y(t) = 8 sin(t) + 5. Therefore, the set of parametric equations that describes the same relationship as the given Cartesian equation is:

• x(t) = t
• y(t) = 8 sin(t) + 5