i need answer

Question

sketch the curve by using the parametric equations to plot points . indicate with an arrow the direction in which the curve is traced  as t increases x=sin(t) , y=t^2 , -180<=t <= 180

Answer 1

x=sin(t), y=t².

t=√y, x=sin(√y); t=-√y, x=-sin(√y).

So the curve has symmetry about the y-axis. It has a pear-drop shape.

-180≤t≤180 which is more appropriately -π≤t≤π, since y=t² when t is measured in radians.

When t=0, x=y=0, so the origin is the point implied.

When t=π, x=0, y=π²=9.87 approx. When t=-π, x=0, y=π². The point (0,9.87) is common to the left and right halves of the curve.

When t=½π, x=1, y=¼π²=2.47 approx, the point (1,2.47). When t=-½π, x=-1, y=¼π²=2.47 approx, the point (-1,2.47).

From this information we can see the direction of the curve. It starts at (0,π²), then travels down to the origin via the left-hand part of the curve.

The origin is the centre of the range of t values (t=0). It then proceeds from the origin up to (0,9.87) via the right-hand part of the curve.