Question

Identify the parametric equations that represent the same path as the following parametric equation.x=4+cos theta y=3sin theta

Answer 1

Option C

• x=4+cos 4θ

,

• y=3 sin 4θ

Explanation:

Parametric equations are commonly used to express the coordinates of the points that make up a geometric object (e.g. a curve or surface), such equations are collectively called a parametric representation.

Given the parametric equation:

`\begin{gathered} x=4+\cos\theta \\ y=3\sin\theta \end{gathered}`

Replace θ with 4θ:

`\begin{gathered} x=4+\cos4\theta \\ y=3\sin4\theta \end{gathered}`

The parametric equation that represents the same path as the given parametric equations is Option C.