Note-taking Guide Lesson 8.2 Ellipses
Key Elements of an Ellipse:
Horizontal Transverse Axis
Vertical Transverse Axis
Equation:
Equation:
Center:
Center:
Foci:
Foci:
Vertices:
Vertices:
Eccentricity:
Eccentricity:
Test Your Skills:
Find the equation of an
1
7.03 Series and Summations
Definition of Series
A series is the sum of a sequences and an easy to represent the sum of terms is using
n
summation notation
a i=a +a + a a
i=l
1
2
3
n
i=
n=
l=
Properties of Sums
Summations follow properties of traditi
8.01 Parabolas
A parabola is the set of all points (x, y) that are equidistant from a fixed line _
and a fixed point _ not on the line.
The _ of a parabola is the midpoint between the focus and the directrix.
The _ of a parabola is the line that passes th
Lesson 7.02 Geometric Sequences
Definition of Geometric Sequence
A sequence is geometric if the ratios of consecutive terms are the _.
= r,
= r,
= r. r _
The number r is the _ _ of the sequence.
2, 4, 8, 16 is a geometric sequence with a common ratio of _
1
7.04 Mathematical Induction
The Principal of Mathematical Induction
Let Pn be a statement involving the positive integer n. We must show the following three
statements in order for the proof to be complete.
1. Show true for n=1.
Step 1: Sub in 1 for n o
Note-taking Guide Lesson 8.3 Hyperbolas
Key Elements of a hyperbola:
Horizontal Transverse Axis
Vertical Transverse Axis
Equation:
Equation:
Center:
Center:
Foci:
Foci:
Vertices:
Vertices:
Asymptotes:
Asymptotes:
Test Your Skills:
Find the standard form o
1
7.01 Arithmetic Sequences
Definition of an Infinite/Finite Sequence
An infinite sequence is a_ _
_. The terms of a sequence are _ denoted by
_. A finite sequence has a domain that consists of
_.
Alternating Sequence
Alternating sequences occur when the
2.06 Rational Functions
Key words
Rational Function
Definitions/ Example
Horizontal and Vertical
Asymptotes
The definition of vertical and horizontal
asymptotes states:
1.
(video on HA and VA
http:/youtu.be/_qEOZNPce60
)
Asymptotes of a Rational
Function
1
6.04 Dot Product of Vectors
Dot Product
Definition:
_
> Test your skills<
Find each dot product.
Show work
a. <-2,-7> <-3,4>
b. <9,5> <0,8>
Properties of the Dot Product
Let u, v, and w be vectors in the plane or in space and let c be a scalar.
1.
2.
3.
4.01 Angles and Their Measure
Keywords
Angle
Definitions/Examples
Initial side:
Terminal Side:
Vertex:
Copy 3
images from
lesson
Standard Position:
Positive Angle:
Coterminal Angles:
Negative Angle:
Radian
Measures
We measure an angle by stating the amoun
4.02 Trigonometric Functions of Acute Angles
Keywords
Right Triangle
Definitions/examples
Hypotenuse:
Opposite side:
Adjacent Side:
Six Trigonometric Functions
http:/youtu.be/5tp74g4N8E
Y
Test your skills
Determine the six trigonometric functions for the
6.01 Law of Sines
Standard notation for labeling a Triangle
Label the triangle below based off of the one in the lesson.
Solving an _triangle requires knowledge of one _ and
any _ other parts of the triangle: _sides, _ angles, or
one angle and one side.
T
4.04 Trigonometric Functions of Any Angle
Keywords
Definitions of
Trigonometric
Functions of any
Angle
Definitions/examples
Let
be an angle in standard position with (x,y) a point on the
terminal side of
and
r=
Sin=
Cos=
Tan=
Cot=
Sec=
Csc=
Example: If an
4.05a Graphs of Sine and Cosine Functions
Keywords:
Basic Sine
and Cosine
Curves
Definitions/Examples
Sine Curve:
Key points on Maximum and Minimum points:
a Sine or
Cosine Curve
X-axis intercepts
Y-axis intercept
The Standard
Form of the
Equations for
Si
2.04 Complex Zeros
Complex Number
Definition:
Operations with complex The rule for the equality of complex numbers states:
Numbers
The rule for the addition and subtraction of complex
numbers states:
Some of the properties for real numbers are also valid
2.02 Polynomial Functions of Higher Degree
General Features of
Polynomial Graphs
1.
2.
Binomial Theorem
N is even then the graph is _
N is odd then graph is _ shaped
Notes:
http:/youtu.be/1pSD8c
YyqUo
Click link for a video
example on this
theorem.
Pasca
4.03 Trigonometric Functions: The Unit Circle
Keywords
The Unit Circle
Definitions/Examples
Definition of
Trigonometric
Functions
Let x be a real number and (x,y) the point on the unit circle
corresponding to t.
Sin(t)=
Cos(t)=
Tan (t)=
Csc (t)=
Sec(t)=
T
6.05 DeMoivres Theorem and nth Roots
Name
Definitions/Examples
Absolute value of a complex
Number
Trigonometric Form of a
Complex Number
> Test your skills<
Problem
Convert each of the following to trigonometric
form.
a. z = 2 + 2i3
b. z = 4i
Now, convert
1
6.02a Law of Cosines
If you are given three _or two _and its included angle,
the ratios would be incomplete. To solve those types of problems, we need the Law of
_.
Law of Cosines
Standard Form
1.
2.
3.
Alternate Form
1.
2.
3.
Three Sides (SSS)
Law of C
1
6.03 Vectors in the Plane
Definition of a Vector
A vector is a_ _ _. The
directed line segment PQ has _ point P and _ point Q.
Its length is shown by |PQ|.
Equivalence
Equivalent if they have the same _and the same
_.
To show that two vectors are equiva
4.07 Inverse Trigonometric Functions
Keywords
Inverse Sine
Function
Definitions/Examples/Notes
Definitions/Examples/Notes:
For this domain, the following properties exist:
1.
2.
3.
1
Definition of
Inverse Sine
Function
The inverse sine function is defined
2.07 Graphs of Rational Functions
Keyword
The Graph of a
Rational
Function
Definition/ Example
1.
2.
3.
4.
5.
For example, for the function f(x) = 5/(x + 1), we can determine the
following:
y-intercept is:
x-intercept is:
vertical asymptote is:
horizontal
2.01 Quadratic Functions
Word
Polynomial Function
Definition/examples
Definition:
Quadratic Function
(Standard Form)
Definition:
Example:
Vertex Form
Definition:
Example:
Put the following into standard quadratic function form.
Find the vertex point and t
1
2.03 Real Zeros of Polynomial Functions
Long Division
Write down steps for video example:
Example click:
http:/virtualnerd.com/algebra1/rational-expressionsfunctions/polynomial-longdivision-example.php
Division Algorithm
What does it state?
Synthetic Di
4.06 Graphs of other Trigonometric Functions
Keywords
The Standard Form of
the Tangent Function
Definitions/ examples
Definitions/ examples/notes
About the Graph of the
Tangent Function
Definitions/ examples/notes
Summary of How to
Graph the Tangent by
Ha