The parametric equation are and
over the interval
Observe that
So
Construct a table with different values of .
![]() | \
![]() | \
![]() | \
![]() | \
![]() | \
![]() | \
![]() | \
![]() | \
![]() | \
![]() | \
![]() | \
![]() | \
![]() | \
![]() | \
![]() | \
![]() | \
![]() | \
![]() | \
![]() | \
![]() | \
![]() | \
![]() | \
![]() | \
![]() | \
Graph :
\(1) Draw the coordinate plane.
\(2) Graph the equations and
for
.
\
Indicate the obtained points on the graph.
\\
Based on the values of , indicate the direction of
as it increases with an arrow.
(b)
\The parametric equation are over the interval
.
Let us take .
\
Substitute in
.
\
.
Therefore, the Cartesian equation is .
(a)
\Graph :
\\
\
(b)
\The Cartesian equation is .