PARABOLAS:
There are 2 ways an equation for a parabola can be written:
I.
y = a ( x h) + k
2
or
( y k ) = a ( x h)
2
Axis of symmetry: x = h
Vertex: ( h, k ) minimum point, if a > 0
maximum point, if
3-5: The Graph Scale-Change Theorem
Pre Calc I (CP)
_
SCALE CHANGE = a stretch or shrink applied to the graph
Ex. 1: Think back to translations. How do you think you might write the rule for a scale c
4-4 Basic Identities Involving Sine, Cosine, and Tangent
PYTHAGOREAN IDENTITY: For every , cos2 + sin2 = 1
*This theorem relates the Pythagorean theorem to the identity (1)
Ex. Let =
cos
p
6
p
3
=
6
2
3-1: Changing Windows
Pre Calc I (CP
_
Transformation: a one to one correspondence between sets of points such as a
translation or a scale change.
The window on the calculator that you choose can make
4-3 Sines, Cosines, and Tangents
Uses in Geometry:
SOH CAH TOA
Used with right triangles
Sin/Cos/Tan called trigonometric functions because they assume that the
angle measure is between 0 degrees and
4-5 Exact Values of Sine, Cosine, and Tangent
RECALL: All Students Take Calculus
Q1
+
+
+
*ALL positive
ALL
SINE (y)
COSINE (x)
TANGENT
Q2
+
*Sine positive
Students
Q3
+
*Tangent positive
Take
Q4
+
*
3-2: The Graph Translation Theorem
Pre Calc I (CP)
_
EX 1: Write a rule for translating the point (x,y) 8 units down and 5 right:
(x, y) (x + 5, y 8)
Define: TRANSLATION = slide transformation
EX 2: L
3-3: Translations of Data
Pre Calc I (CP)
_
EX 1: Suppose a small class yields the following set of test scores:
87, 86, 85, 81, 78, 75, 75, 73, 70, 68, 67, 63.
(a) Find the measures of central tenden
Viewing Solids and Surfaces Exam Review
Views/elevations planar view of 3-dimensional figures given from top, front, or sides
*2-dimensional picture (projection) of a 3-dimensional figure
EX 1 Sketch
->-
C
CB
' Q»
E
D
a;
i
a
t
2
ED
H
.E
D7
- :5
D
:5;
w.
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C
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52
.2
C5
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E
_u
3
a
U5
2
D
5.7.)
U
E
>
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.C
.9
>1
:1
D
U
993
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Name M
Quiz 1-
, For use after Lessans 7.17.2
Find the u
The Pythagorean Theorem Study Guide
Square Roots:
Given the area of a square (A), the side of a square (s) is the square root of the area.
s A
EX 1: What is the length of a side of a square whose area
Tangent WS
TAN A =
OPPOSITE
ADJACENT
Find the length of the missing side by setting up a tangent ratio.
1.
2.
3.
61
x
21
12
32
72
x
50
TAN-1 FINDS AN ANGLE MEASURE
Find the measure of the indicated an
Pyramids & Cones Notes
pyramid: surface of a conic solid whose base is a polygon.
cone: surface of a conic solid whose base is a circle.
PYRAMIDS:
Have one base (polygon) and a vertex (not two bases)
Tangent Notes
TAN A =
OPPOSITE
ADJACENT
Find the length of the missing side by setting up a tangent ratio.
1.
2.
3.
61
x
21
12
32
72
x
50
x
50
50 tan 32 = x
x
x
12
12 tan 61 = x
tan 32 =
x = 31.24
21
Overview of Surface Area and Volume
What is SURFACE AREA? The measure of how much (2-dimensional) area covers a (3dimensional) space
How can we calculate surface area for a 3-Dimensional figure? Add u
Areas of Trapezoids Notes
Trapezoid Area Formula:
Geometry (CP)
1
A h(b1 b2 )
2
h is the height of the altitude - must form a right angle with a base.
b1 and b2 are the bases (remember, they are diffe
3/2/2012
I. Vocabulary:
A.AngleofDepression:anglemeasured
lookingdownfromthehorizontal.
Angle of Depression
5.1:TrigonometricRatiosinRight
Triangles
g
B.AngleofElevation:anglemeasured
lookingupfromthe