Question

# Identify the parametric equations that represent the same path as the following parametric equations. show your work x=3+ cos theta y= 2 sin theta A. x=3+cos 2 theta y=2sin 2theta B.x=cos theta y=3+2sin theta C. x=3+2 cos theta y= 4 sin theta D. x=2 sin theta y= 3+cos theta I know it’s A but i’m not sure how to do the work :(

Answer

A. x=3+cos 2theta y=2sin 2theta

- Recognize the original parametric equations: x=3+ cos theta y= 2 sin theta.
- Substitute in the double angle identities for cosine and sine: x=3+cos 2theta y=2sin 2theta.
- Compare to given answer choices: A. x=3+cos 2theta y=2sin 2theta, B. x=cos theta y=3+2sin theta, C. x=3+2 cos theta y= 4 sin theta, D. x=2 sin theta y= 3+cos theta.
- Determine that A is correct because it matches the parametric equations from step 2.