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Cogito

Precalculus · Chapter 7 · Lesson 1

Practice Worksheet

Parametric Equations

Let a third variable drive both coordinates.

12 problems · about 22 minutes · TEKS P.3.C, TEKS P.3.E

NameDate

Figure — use these to answer the problems

x = cos t and y = sin t traces this circle. The angle is the parameter, and moving it moves the point.
(0.707, 0.707)
  • Angle45° = π/4 rad
  • x-coordinate0.707
  • y-coordinate0.707
  • cos 45°0.707
  • sin 45°0.707
t, the parameter in degrees45
Figure 1

Warm Up

Straightforward practice. Get the method working first.

5 problems

  1. x = t − 1, y = 3t. What is y when t = 5?

    Answer

  2. What is lost when the parameter is eliminated?

    • The direction of travel and any restriction on t.
    • The shape of the curve.

  3. x = 2t, y = t². What is x when t = 3?

    Answer

  4. Same equations. What is y when t = 3?

    Answer

  5. x = t + 5, y = t. What is y when x = 9?

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. x = cos t, y = sin t. What is x² + y²?

    Answer

  2. x = 4t, y = 8t. Eliminating t gives y = kx. What is k?

    Answer

  3. x = t, y = t². Eliminating t gives y = xⁿ. What is n?

    Answer

Stretch Yourself

Mixed problems. Work out what kind of question it is before you start.

4 problems

  1. What does a parametric form carry that a rectangular one does not?

    • The direction of travel
    • When the object reaches each point
    • The shape of the path
    • Nothing extra at all
    • Tick every box that applies.

  2. x = 5t, y = 3t. What is y when t = 2?

    Answer

  3. The Position

    x = 3t and y = t + 2. What is x when t = 4?

    Answer

  4. The Other Coordinate

    Same equations. What is y when t = 4?

    Answer