Chapter 6 Review

1
Chapter 6 Review Due 5/21
2 22 even 53 59 odd 62 70 even 74,
81, 86 (p. 537)
2
Vector Formulas
Unit Vectors
Horizontal/Vertical components
Angle between Vectors
Projections
3
6.1 Vectors in a Plane Day 1
4
direction
magnitude (size)
force
acceleration
velocity
Starts at (0, 0) and goes to (x, y)
5
equivalent
6
(No Transcript)
7
Vector addition
Vector multiplication (multiplying a vector by a
scalar or real number)
sum
terminal
initial point
point
parallelogram law
8
unit vector
unit vector
direction
9
direction angle
10
25o
11
6.2 Dot Product of Vectors Day 1
12
dot product
work done
vectors
scalar (real number)
13
Theorem Angles Between Vectors
If ? is the angle between the nonzero vectors
u and v, then
14
Proving Vectors are Orthagonal
15
Proving Vectors are Parallel
The vectors u and v are parallel if and only
if u kv for some constant k
16
Proving Vectors are Neither
If 2 vectors u and v are not orthagonal or
parallel then they are NEITHER
17
vector projection
18
Unit Circle
19
6.4 Polar Equations Day 1
20
polar coordinate system
pole
polar axis
( r, ? )
polar coordinates
directed distance
directed angle
polar axis
line OP
21
(No Transcript)
22
Cartesian (rectangular)
Polar
pole
origin
polar axis
positive x axis
x r cos ?
y r sin ?
23
so
so
24
Helpful Hints

• Polar to Rectangular
• multiply cos? or sin? by r so you can convert to
  x or y
• r2 x2 y2
• re-write sec? and csc? as
• complete the square as necessary

• Rectangular to Polar
• replace x and y with r?cos? and r?sin?
• when given a squared binomial, multiply it out
• x2 y2 r2

(x a)2 (y b)2 c2 Where the center of the
circle is (a, b) and the radius is c
25
6.5 Graphs of Polar Equations Day 1
26
(No Transcript)
27
(No Transcript)
28
ANALYZING POLAR GRAPHS

• We analyze polar graphs much the same way we do
  graphs of rectangular equations.
• The domain is the set of possible inputs for ?.
  The range is the set of outputs for r. The
  domain and range can be read from the trace or
  table features on your calculator.
• We are also interested in the maximum value of
  . This is the maximum distance from the pole.
  This can be found using trace, or by knowing the
  range of the function.

• Symmetry can be about the x-axis, y-axis, or
  origin, just as it was in rectangular equations.
• Continuity, boundedness, and asymptotes are
  analyzed the same way they were for rectangular
  equations.

29
What happens in either type of equation when the
constants are negative? Draw sketches to show
the results.

• Rose Curve when a is negative
• (n cant be negative, by definition)

• if n is even, picture doesnt changejust the
  order that the points are plotted changes
• if n is odd, the graph is reflected over the x
  axis

30
What happens in either type of equation when the
constants are negative? Draw sketches to show
the results.

• Rose Curve when a is negative
• (n cant be negative, by definition)

• if n is even, picture doesnt changejust the
  order that the points are plotted changes
• if n is odd, the graph is reflected over the y
  axis

31
What happens in either type of equation when the
constants are negative? Draw sketches to show
the results.

• Limacon Curve when b is negative (minus in
  front of the b)
• (a cant be negative, by definition)

• when r a bsin?, the majority of the curve is
  around the positive y axis.
• when r a bsin?, the curve flips over the x
  axis.

32
What happens in either type of equation when the
constants are negative? Draw sketches to show
the results.

• Limacon Curve when b is negative (minus in
  front of the b)
• (a cant be negative, by definition)

• when r a bcos ?, the majority of the curve
  is around the positive x axis.
• when r a bcos ?, the curve flips over the y
  axis.