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Warm-Up 1/16 1. 2. C Assignments Questions? H

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Rigor: You will learn how to graph parametric equations and how to write equations in rectangular form. Relevance: You will be able to use parametric equations to solve real world problems related to the motion of projectiles. MA.912. A.2.11

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**7-5 Parametric Equations**

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**The variable t is called a parameter.**

The values of t trace the curve in a specific direction called the orientation.

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**Example 1: Sketch the curve given by each pair of parametric equations over the interval.**

a. ๐ฅ= ๐ก 2 +5 and ๐ฆ= ๐ก 2 +4;โ4โค๐กโค4 t x y โ 4 โ 3 โ 2 โ 1 1 2 3 4 21 2 14 2.5 9 3 6 3.5 5 4 6 4.5 9 5 14 5.5 21 6

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**Example 1: Sketch the curve given by each pair of parametric equations over the interval.**

b. ๐ฅ= ๐ก and ๐ฆ= ๐ก 4 +4;โ8โค๐กโค8 t x y โ 8 โ 6 โ 4 โ 2 2 4 6 8 21 2 14 2.5 9 3 6 3.5 5 4 6 4.5 9 5 14 5.5 21 6

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Example 1:

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**Example 2: Write the parametric equations in rectangular form.**

๐ฅ=โ3๐ก and ๐ฆ= ๐ก 2 +2 ๐ฅ=โ3๐ก ๐ฆ= ๐ก 2 +2 ๐ฆ= โ ๐ฅ ๐ฅ โ3 =๐ก ๐ฆ= 1 9 ๐ฅ 2 +2 ๐ก=โ ๐ฅ 3

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**Example 3: Write the parametric equations in rectangular form**

Example 3: Write the parametric equations in rectangular form. then graph the equation. State domain restrictions. ๐ฅ= 1 ๐ก and ๐ฆ= ๐ก+1 ๐ก ๐ฆ= ๐ฅ 2 +1 ๐ฆ= 1 ๐ฅ ๐ฅ 2 ๐ฆ= ๐ก+1 ๐ก ๐ฅ= 1 ๐ก ๐ฅ ๐ก =1 ๐ฆ= 1 ๐ฅ ๐ฅ 2 ๐ฅ ๐ฅ 2 ๐ก = 1 ๐ฅ ๐ก 2 = 1 ๐ฅ 2 ๐ฆ= 1+ ๐ฅ 2 ๐ฅ ๐ฅ 2 ๐ก= 1 ๐ฅ 2 D: x >0 ๐ฆ= 1+ ๐ฅ 2 1 ๐ฆ=1+ ๐ฅ 2

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Example 5: Use the parameter to write the parametric equations that can represent ๐ฆ= ๐ฅ 2 โ4. Then graph the equation, indicating the speed and orientation. a. ๐ก=๐ฅ ๐ฅ=๐ก ๐ฆ= ๐ฅ 2 โ4 ๐ฆ= ๐ก 2 โ4 ๐ฆ= ๐ก 2 โ4 b. ๐ก=4๐ฅ+1 ๐ฅ= ๐กโ1 4 ๐ฅ= ๐กโ1 4 ๐ฆ= ๐กโ โ4 ๐ฆ= ๐ก โ ๐ก 8 โ 63 16 ๐ฆ= ๐ก 2 โ2๐ก+1 16 โ 64 16 ๐ฆ= ๐ก 2 โ2๐กโ63 16

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**โ1 math! 7-5 Assignment: TX p469, 2-16 Even & 26-36 Even**

only graph 2-8 not 32 Chapter 7 Test Thursday 1/23 You will need to know formulas.

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**Example 4: Write the parametric equations in rectangular form**

Example 4: Write the parametric equations in rectangular form. then graph the equation. ๐ฅ=2 cos ๐ and ๐ฆ=4 sin ๐ cos ๐ = ๐ฅ 2 sin ๐ = 4 4 sin 2 ๐ + cos 2 ๐ =1 ๐ฅ ๐ฆ =1 ๐ฅ ๐ฆ =1

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