Question

Comparing the polar equations r = 1 + cos(0) and r = 1 + sin(0), what is the * 1 point
primary difference in their geometric representations, and what causes this difference?
The first is rotated 90° counterclockwise relative to the second because cosine and sine functions are phase-shifted by n/2 radians
The first is symmetric about the polar axis while the second is symmetric about the
line 0 = t/2, due to the phase difference between cosine and sine
• The first has a larger area because cosine produces larger values than sine
• The first is a cardioid while the second is a different type of limaçon

Answer 1

Correct answer (concise): The two curves are the same cardioid but rotated by 90° (π/2). r = 1 + cosθ is symmetric about the polar (x)‑axis; r = 1 + sinθ is symmetric about the line θ = π/2 (y‑axis). This difference is caused by the phase shift sinθ = cos(θ − π/2).

Notes: both are cardioids (so option 4 is wrong) and they have the same area (so option 3 is wrong).