Problem $4.$ Given the parametric curve:

$x=1+2cos(t)$;$,y=2+2sin(t)$

a$)$ Sketch the curve represented by the set of parametric equations and write the corresponding rectangular equation by eliminating the parameter $t$;

$[$Hint$1$: Fill in the table and use the data to plot the points on the xy$-$coordinate system provided. Indicate the direction on the curve. Hint$2$: To eliminate $t$ isolate the trig functions and square both sides. Then add the two equations.$]$

$\backslash$table$[[t,,,,,],[x,,,,,],[y,,,,,]]$

b$)$ Find the equation of the tangent line $tq,$ corresponding to $t=\frac{}{6}.$

c$)$ Using the parametric equation for arc length find the length of the curve for $0t.$