Parametric Equations - Kuta Software

Kuta Software - Infinite Precalculus

Name___________________________________

Parametric Equations

Date________________ Period____

Sketch the curve for each pair of parametric equations.

1) xt, yt

y

2) xt, yt , t

y

x

x

3) xsin t, ycos t

y

x

4) xsec t, ytan t

y

x

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Worksheet by Kuta Software LLC

Write each pair of parametric equations in rectangular form.

5) x t , yt

6) xt, yt t

7) xt, ytt

8) xsin t, ycos t

9) xsec t, ytan t

10) xcos t, ysin t

Use the parameter to write each rectangular equation as a pair of parametric equations.

11) x y , t y

12) y x x, t x

Critical thinking questions: 13) Write a set of parametric equations that represent yxx. 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 yx. 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) xt, yt

y

t

t

t

t

t

t

t

t

ttt x

2) xt, yt , t

y

t

t

t

x

t

t

t

3) xsin t, ycos t

y

t

t

t

t

t

t t

x

t

4) xsec t, ytan t

y

t

t

t

t

t x

t

-1-

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Worksheet by Kuta Software LLC

Write each pair of parametric equations in rectangular form.

5) x t , yt

6) xt, yt t

x y

y x x

7) xt, ytt

y x x

8) xsin t, ycos t x y

9) xsec t, ytan t x y

10) xcos t, ysin t

(x) ( y)

Use the parameter to write each rectangular equation as a pair of parametric equations.

11) x y , t y

12) y x x, t x

xt , yt

xt, y t t

Critical thinking questions:

13) Write a set of parametric equations that represent yxx. Then write a second set of parametric equations that represent the same function, but with a slower speed

Many answers. Ex: ytt, xt and yt t, x t

14) Write a set of parametric equations that represent yx. 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: yt, xt and yt, xt

Create your own worksheets like this one with Infinite Precalculus. Free trial available at

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Worksheet by Kuta Software LLC

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