1. 2. warm-up 1/16 assignments questions? c h. rigor: you will learn how to graph parametric...
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1.
2.
Warm-Up 1/16
Assignments Questions?
C
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.
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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. and
t x y
– 4
– 3
– 2
– 1
0
1
2
3
4
21
14
9
6
5
6
9
14
21 6
5.5
5
4.5
4
3.5
3
2.5
2
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Example 1: Sketch the curve given by each pair of parametric equations over the interval.
b. and
t x y
– 8
– 6
– 4
– 2
0
2
4
6
8
21
14
9
6
5
6
9
14
21 6
5.5
5
4.5
4
3.5
3
2.5
2
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Example 1:
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Example 2: Write the parametric equations in rectangular form.
and
𝑦=𝑡 2+2
𝑦=(− 𝑥3 )
2
+2
𝑦=19𝑥
2
+2
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Example 3: Write the parametric equations in rectangular form. then graph the equation. State domain restrictions.
and
𝑦=
1
𝑥2 +1
1𝑥2
𝑥√𝑡=1
√𝑡= 1𝑥
(√𝑡 )2=( 1𝑥 )
2
𝑡=1
𝑥2
𝑦=
1𝑥2 +
𝑥2
𝑥2
1𝑥2
𝑦=
1+𝑥2
𝑥2
1𝑥2
𝑦=1+𝑥2
1𝑦=1+𝑥2
D: x >0
𝑦=𝑥2+1
𝑦=𝑡+1𝑡
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Example 5: Use the parameter to write the parametric equations that can represent . Then graph the equation, indicating the speed and orientation.
a.
𝑦=𝑥2− 4𝑦=𝑡 2− 4
𝑦=𝑡 2− 4
b.
𝑥=𝑡−1
4
𝑦=( 𝑡− 14 )
2
− 4
𝑦= 𝑡2 −2 𝑡+116
−6416
𝑦= 𝑡2 −2 𝑡−6316
𝑥=𝑡−1
4
𝑦= 𝑡2
16−𝑡8
−6316
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√−1math!
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. then graph the equation.
and
cos𝜃=𝑥2 sin 𝜃=
44
sin2𝜃+cos2𝜃=1
( 𝑥2 )2
+( 𝑦4 )2
=1
𝑥2
4+ 𝑦2
16=1