Nice job here, finding the slope and then using point slope form to get the tangent line.
Simplify when possible! At the end you should see that there's a common factor of 2/3.
No one nailed this one. The two equations x=0 and y=0 must be solved simultaneously, to yield t is an integral multiple of pi. This gives two solutions (there are two values of cos(x) when sin(x)=0: cos(x)=1 and cos(x)=-1). These represent the two ways in which the curve passes through the origin in the graph, along two different tangents: y=0 and y=2x.
The slopes of the tangents are determined using the equation dy/dx, and the special values of t.