Question

find the equation of the circle r(t) = ti+sin t j at point (pi/2, 1)
the point value is pi/2 since r(pi/2) = pi/2i + sin pi/2j is
pi/2i + j

Answer 1

\[r(t) = t\hat\imath+\sin t \hat\jmath\] \[P= \left(\frac\pi 2, 1\right)\]
\[r\left(\frac\pi2\right) = \frac\pi2\hat\imath + \sin \frac\pi2\hat\jmath=
\frac\pi2\hat\imath +\hat\jmath\]