math3b_HWch10_parametric_polar - Berkeley City College...

Berkeley City College HW - Chapter 10 - Parametric Equations and Polar Coordinates
Due :________________
Name___________________________________
Parametric equations and a parameter interval for the motion of a particle in the xy - plane are
given. Identify the particle's path by finding a Cartesian equation for it. Graph the Cartesian
equation. Indicate the portion of the graph traced by the particle and the direction of motion.
1) x = 4 cos t, y = 4 sin t, ! ≤ t ≤ 2 !
x
-4 -3 -2 -1 1 2 3 4
y
5
4
3
2
1
-1
-2
-3
-4
-5
x
-4 -3 -2 -1 1 2 3 4
y
5
4
3
2
1
-1
-2
-3
-4
-5
2) x = 2 sin t, y = 3 cos t, 0 ≤ t ≤ 2 !
x
-4 -3 -2 -1 1 2 3 4
y
5
4
3
2
1
-1
-2
-3
-4
-5
x
-4 -3 -2 -1 1 2 3 4
y
5
4
3
2
1
-1
-2
-3
-4
-5
Instructor K. Pernell 1

3) x = 25t
2
, y = 5t, - ∞ ≤ t ≤ ∞
x
-4 -3 -2 -1 1 2 3 4
y
5
4
3
2
1
-1
-2
-3
-4
-5
x
-4 -3 -2 -1 1 2 3 4
y
5
4
3
2
1
-1
-2
-3
-4
-5
Obtain the Cartesian equation of the curve by eliminating the parameter.
4) x = t , y = 2t + 8
5) x = 3 t - 7 , y = 9 8 - t
6) x = t
3
- 5t, y = t
2
- 5
2

7) x = 9 sin
2
t, y = 9 cos
2
t; 0 ≤ t ≤ 2 !
Find dy/dx without eliminating the parameter.
8) x = 5t
2
, y = 11 t
3
; t ≠ 0
9) x = 6 tan t - 2, y = 4 sec t + 3, t ≠
(2n + 1) !
2
10) x = ln(2t), y = e
2t
11) x = 1/t
6
, y = - 3 + ln t
Find d
2
y/dx
2
without eliminating the parameter.
12) x = 5t
2
, y = 10 t
3
; t ≠ 0
3

13) x = 1 - 2 sin t, y = 1 + 7 cos t, t ≠ n !
14) x = ln(2t), y = ln(8t)
3
, t > 0
15) x =
t
2
2
+ 8t, y =
t
2
2
- 2t, t ≠ - 8
Find an equation for the line tangent to the curve at the point defined by the given value of t.
16) x = sin t, y = 6 sin t, t =
!
3