The matrix R(t) is defined by `R(t)=[(cos t,sin t),(-sin t,cos t)]`. Show that `R(s)R(t)=R(s+t)`.

The matrix R(t) is defined by R(t) = [(cost , sin t),(-sint,cost)] . Show that R(s) R(t) = R(s+t).

x = a (cos t + sin t), y = a (sin t-cos t)

If x=a(cos t+t sin t) and y=a(sin t-t cos t)

x=e^t (sin t + cos t ),y=e^t(sin t -cos t)

7. x=a(cos t+t sin t),y=a(sin t-t cos t) find dy/dx

Find (dy)/(dx) if x =a ( cos t + t sin t ), y = a ( sin t - t cos t).

Prove that the curve represented by x=3(cos t+sin t),y=4(cos t-sin t),t in R is an ellipse

The displacement vector of a particle of mass m is given by r (t) = hati A cos omega t + hatj B sin omega t . (a) Show that the trajectory is an ellipse. (b) Show that F = -m omega^(2)r .