Math 25 Trigonometry November 17, 1999

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Math 25 --- Trigonometry November 17, 1999

• Section 5.4 questions
• Section 5.5
• Break
• Section 6.2
• Assignments 26 and 27

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AnnouncementsNovember 17, 1999

• Trig Notebooks due December 1.
• Exam 4 Monday November 22
• Chapter 5 and Appendix 4

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Unit Vectors
A vector u for which u1 is called a unit
vector. The unit vector in the x-direction is
labeled i. The unit vector in the y-direction is
labeled j. The vector v in the plane can be
written v aibj where a and b are real numbers.
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Vector Properties
Given vectors vaibj and wcidj, and scalar a.
Then, the following properties hold. vw
(ac)i(bd)j v-w (a-c)i(b-d)j av
(aa)i(ab)j v
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Unit Vector in the Direction of v
For any nonzero vector v, the vector is a unit
vector that has the same direction as v.
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Vectors given a Magnitude, v, and Direction, a
v r
a
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Dot Product
Given vectors vaibj and wcidj, the dot
product, , is defined as Notice,
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Angle Between Vectors
Given vectors u and v the angle between the
vectors is given by
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Definition of a Parabola
A parabola is defined as the collection of all
points P(x,y) in the plane that are the same
distance from a fixed point F as they are from a
fixed line D. The point F is called the focus of
the parabola, and the line D is its directrix.
As a result, a parabola is the set of points for
which
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Equations of a Parabola
Vertex at
Horizontal Directrix
Focus opens up, - opens down
Vertical Directrix
Focus - opens left, opens right
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Assignment 26 and 27

• Homework 5.5 pbs 1-11 (odd)
• Homework 6.2 pbs 5-65 (every 5th), 67, 69