$Q5.$

$(a)$ Consider the parametrically defined curve, $(x,y)=(3sin(t+\frac{}{3})-1,4sin(3t+\frac{}{2})).$

Determine all points where the tangent line $to$ the curve $is$ horizontal. Determine all points

where the tangent line $to$ the curve $is$ vertical.

$(b)$ Use the two different ways $we$ learned $in$ the lessons $of$ COORD $-Gto$ calculate the area $of$ the

loop $in$ the curve

$(x,y)=(t^3-4t-5,4-3t^2)$

$To$ earn full marks $be$ sure $to$ clearly state any formulas $we$ have learned $in$ our lessons before

applying them.