<s>[INST] Parametric equations including addition So I am familiar with finding the parametric equation given multiplicative $x$ and $y$ values but in a problem such as
$x=2+\cos(t)$,
$y=3+\sin(t)$, 
$0\le t \le \frac{5\pi}{2}$
I cannot even make of what I am supposed to do to find what type of graph this will be on nor its direction.
 [/INST] community wiki post so that the question can be closed
To expand on what was said in the comments, we have
\begin{align*}
x & = 2 + \cos t\\
y & = 3 + \sin t\\
\end{align*}
where $0 \leq t \leq \frac{5\pi}{2}$.  
We eliminate $t$.
\begin{align*}
x - 2 & = \cos t\\
y - 3 & = \sin t
\end{align*}
Squaring each equation and adding yields 
$$(x - 2)^2 + (y - 3)^2 = \cos^2t + \sin^2t$$
Using the Pythagorean Identity $\cos^2t + \sin^2t = 1$ yields
$$(x - 2)^2 + (y - 3)^2 = 1$$
which is the equation of a circle with radius $1$ and center $(2, 3)$.  For the entire circle to be traversed, the interval in $t$ must have length at least $2\pi$.  Since $\frac{5\pi}{2} > 2\pi$, the entire circle is traversed.  In fact, it is traversed 
$$\frac{\frac{5\pi}{2}}{2\pi} = \frac{5\pi}{2} \cdot \frac{1}{2\pi} = \frac{5}{4}$$ 
times.  
 
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