Calculus Parametric Equations (God bless you)?

Use a graphing calculator to find the point at which curve C defined bt 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.

Calculus Parametric Equations (God bless you)?
If you plot the curve on the calculator, it seems that it crosses itself at the origin. On the TI83/84, set the MODE to PAR, then put X1t = sin(t) and Y1t = sin(t + sin(t)). Hit ZOOM TRIG to get the curve.





a) Since it appears that the curve crosses itself at (0,0), find t such that x=0, ie, sin(t) =0. THis happens at 0 and π (and all multiples). You should verify that y is also zero at these values of t.





b) The question tells you that the answer to a) is indeed the origin!!. To get the eqn of the line, you need the slope, which is dy/dx. For parametric eqns, dy/dx = dy/dt / dx/dt. You also need a point, which is (0,0), so use the point slope formula for the line.





I will let you find dy/dt and dx/dt, which you need to evaluate at t=0 and t=π