Consider the parametric equation of a curve:
x=cos(t), y= 1- sin(t), 0 ≤ t ≤ π
Part (a): Find the Cartesian equation of the
curve by eliminating the parameter. Also, graph the curve and
indicate with an arrow the direction in which the curve is traced
as the parameter increases. Label any x and y intercepts.
Part(b): Find the point (x,y) on the curve with
tangent slope 1 and write the equation of the tangent line.
f(x,y)=sin(2x)sin(y)
intervals for x and y:
-π/2 ≤ x ≤ π/2 and -π ≤ y ≤ π
find extrema and saddle points
In the solution, I mainly interested how to
findcritical points in case of the system of trigonometric
equations (fx=0 and fy=0).
,
y (x , t)= A sin (k x − ω t )
calculate the vertical position y in [cm], vertical speed vy in
[m/s] and vertical acceleration ay in [m/s2] of the wave that the
wave driver generated at x = 15 cm and at time t = 3 s during trial
5 of this experiment. Assume that A = 2 cm. The other values in the
equation can be calculated from the experimental data. Remember to
differentiate the above...