Please help me on this question. (BIG GRADE FOR ME ) thankssss?

Use a graphing calculator to find the point at which curve C defined by parametric equations x=sin t , y=sin(t+sint), crosses itself for two different values of t.





a)Find and state the two values of t.


b). Show that C has two tangent lines at the origin and find their equations.

Please help me on this question. (BIG GRADE FOR ME ) thankssss?
a: sin t=0 if t=πk, k∈Z. Thus, x=sin t=0 and y=sin (t+sin t)=sin (t+0)=sin t=0. Therefore, and two solutions of the form t=πk will work, you might choose e.g. t=0 and t=π





b: Since the line passes through the origin, the equation of the line is simply y=mx, where m is the slope of the line at the origin. The slope is given by (dy/dt)/(dx/dt), which is given by cos (t+sin t) (1+cos t)/cos t. For t=0, this is 2, but for t=π, this is 0. Therefore, there are two tangent lines running through the origin, with equations y=2x and y=0.





As for the graphing part, this function has a really nice graph, so I've uploaded it here: http://img161.imageshack.us/img161/1597/... . I think that the nature of the problem is made very much clearer by the graph.
Reply:a) t=0 %26amp; t= 6.28319


b) The first tangent at t=o its equation is : y=0


The second tangent at t = 6.28319


Its slope = sin(t+sint)/ sin t = 1.017346621


its equation is : y = 1.017346621 x