SSCE HSC Mathematics Extension 1 Expansion of (1 + x)^n, Pascal’s triangle: The diagram shows a semicircle.

Option A: corresponds to shifting vertically but does not fit.
Option B: uses cosine for x and sine for y, fitting the quadrant and the semicircle.

Question

The diagram shows a semicircle.

Which pair of parametric equations represents the semicircle shown?

A.  $
\begin{cases}
 x = 3 + \sin t \
 y = 2 + \cos t \
 	ext{for } \frac{\pi}{2} \leq t \leq \pi 
\end{cases}$

B.  $
\begin{cases}
 x = 3 + \cos t \
 y = 2 + \sin t \
 	ext{for } \frac{\pi}{2} \leq t \leq \pi 
\end{cases}$

C.  $
\begin{cases}
 x = 3 + \sin t \
 y = 2 - \sin t \
 	ext{for } \frac{\pi}{2} \leq t \leq \pi 
\end{cases}$

D.  $
\begin{cases}
 x = 3 + \cos t \
 y = 2 - \sin t \
 	ext{for } \frac{\pi}{2} \leq t \leq \pi 
\end{cases}$

The diagram shows a semicircle - HSC - SSCE Mathematics Extension 1 - Question 9 - 2021 - Paper 1