Kuta Software - Infinite Precalculus
Name___________________________________
Parametric Equations
Date________________ Period____
Sketch the curve for each pair of parametric equations.
1) xt, y
t

2) xt, y




y











 x









y









 x


 x
4) xsec t, ytan t


y






3) xsin t, ycos t


t 
 , t



 x




y









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Worksheet by Kuta Software LLC
Write each pair of parametric equations in rectangular form.
5) x
t
, yt

7) xt, yt  t
9) xsec t, ytan t
t  t 
6) xt, y    

 


8) xsin t, ycos t
10) xcos t, ysin t
Use the parameter to write each rectangular equation as a pair of parametric equations.
11) x
y
, ty

12) y
x
x 
 x, t  

 
Critical thinking questions:

13) Write a set of parametric equations that represent yx x. Then write a second set of
parametric equations that represent the same function, but with a slower speed

14) Write a set of parametric equations that represent yx . Then write a second set of parametric
equations that represent the same function, but with a faster speed and an opposite orientation.
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Worksheet by Kuta Software LLC
Kuta Software - Infinite Precalculus
Name___________________________________
Parametric Equations
Date________________ Period____
Sketch the curve for each pair of parametric equations.
1) xt, y
t

2) xt, y



t

t

t

t
y

t

t

y
t 
 , t


t
t
t
 tt


t

 x


t






t





3) xsin t, ycos t

y


t




t



t

 x





t
t





t


t



t



t
 x
y


t

t




4) xsec t, ytan t


t

t
 x
t
t



t







t


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Worksheet by Kuta Software LLC
Write each pair of parametric equations in rectangular form.
5) x
t
, yt

x
t  t 
6) xt, y    

 
y

y
7) xt, yt  t


8) xsin t, ycos t

10) xcos t, ysin t
9) xsec t, ytan t


x
y
  


x
y  x


x 
x  x 
   



( x) 
y



 
( y) 


Use the parameter to write each rectangular equation as a pair of parametric equations.
11) x
y
, ty

12) y
t
x , yt

x
x 
 x, t  

 
xt, y
t  t 
   
 

Critical thinking questions:

13) Write a set of parametric equations that represent yx x. Then write a second set of
parametric equations that represent the same function, but with a slower speed

t
t

Many answers. Ex: yt t, xt and y  t, x



14) Write a set of parametric equations that represent yx . Then write a second set of parametric
equations that represent the same function, but with a faster speed and an opposite orientation.


Many answers. Ex: yt , xt and yt , xt
Create your own worksheets like this one with Infinite Precalculus. Free trial available at KutaSoftware.com
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Worksheet by Kuta Software LLC