Problems
Problem 1.1:
Is the following plane curve a function:
y = 3t2,
x = ,
0≤t≤5?
[Solution]
Problem 1.2:
The following plane curve is a circle:
x = 2 cos(t),
y = 2 sin(t),
0≤t < 2π. Is its orientation clockwise or couterclockwise? What happens
when you reverse the parametric equations, so that
x = 2 sin(t),
y = 2 cos(t)?
[Solution]
Problem 1.3:
Convert the parametric equation
x = 2t,
y = ,
t > 0, to a
rectangular equation.
[Solution]
Problem 1.4:
Convert the parametric equation
x = 3t + 1,
y = ,
t≠, to a rectangular equation.
[Solution]
Problem 1.5:
How many times does the graph of
x = t2 - t - 6,
y = 2t,
-5 < t < 5 cross
the
y-axis?
[Solution]
Problem 1.6:
Jim and Bob are racing from the origin to the point
(5, 10). Let
t be the
number of seconds after the start of the race. Jim's position at any time
t
is given by the parametric equations
x = t,
y = 2t. Bob's position at any
time
t is given by the parametric equations
x = 5t,
y = 10t. Who will win
the race? How long does it take each competitor to finish the race?
[Solution]
, t > 0, to a
rectangular equation.
[Solution]
, t≠
, to a rectangular equation.
[Solution]
