Question

Match the parametric equations with the correct graph.

1) x = cos(8t), y = sin(8t), z = e⁽⁰·⁸ᵗ⁾
2) x = sin(8t), y = cos(8t), z = e⁽⁰·⁸ᵗ⁾
3) x = cos(8t), y = sin(8t), z = e⁽⁰·⁸ᵗ⁾
4) x = sin(8t), y = cos(8t), z = e⁽⁰·⁸ᵗ⁾

Answer 1

The graph for parametric equation 1) and 2) represents a helix, while the graph for parametric equation 3) and 4) represents an oscillating wave moving in the z direction.

Step-by-step explanation:

1. For parametric equation 1) x = cos(8t), y = sin(8t), z = e⁽⁰·⁸ᵗ⁾ the graph represents a helix.
2. For parametric equation 2) x = sin(8t), y = cos(8t), z = e⁽⁰·⁸ᵗ⁾ the graph represents a helix.
3. For parametric equation 3) x = cos(8t), y = sin(8t), z = e⁽⁰·⁸ᵗ⁾ the graph represents an oscillating wave moving in the z direction.
4. For parametric equation 4) x = sin(8t), y = cos(8t), z = e⁽⁰·⁸ᵗ⁾ the graph represents an oscillating wave moving in the z direction.