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 a > 0
II.
y = ax 2 + bx + c
Axis of symmetry:
x=
b
2a
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 change that
stretches the graph horizontally by a factor
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
sin
p
1
=
6
2
2
2
3 3 1
1
cos + sin = + = + =1
2 4 4
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 the graph look different
EX 1: Graph y = 2x on the fol
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 180 degrees
Uses in Precalculus:
Sin/Cos/Tan called cir
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
+
* Cosine pos
Calculus
KEY POINTS (COS , SIN ) WE ALREADY
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: Let f ( x) =x 2
Let g ( x) =( x +3) 2 +4
(a) Graph each
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 tendency:
(b) Give the 5 number summary:
Mean: 75.667
Min: 63
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 a square pyramid from the front, top, and side
EX 2 Ske
->-
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Name M
Quiz 1-
, For use after Lessans 7.17.2
Find the unknown side length. Write yaur answar in simplest
radic
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 is 25 ft2.
The exact, simplified value of a radical pu
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 angle.
1.
2.
10
3.
x
13
9
x
x
14
EXACT VALUES:
3
30-60-90
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)
Lateral Edges: segment connecting the vertices to the
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
x
x tan 72 = 21
21
x=
tan 72
x = 6.82
tan 61 =
tan 72 =
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 up all of the areas
around the outside of a 3-dimensiona
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 different)
So the area is the altitude times the mean of the
3/2/2012
I. Vocabulary:
A.AngleofDepression:anglemeasured
lookingdownfromthehorizontal.
Angle of Depression
5.1:TrigonometricRatiosinRight
Triangles
g
B.AngleofElevation:anglemeasured
lookingupfromthehorizontal.
Angle of Elevation
B
II.RightTriangleTrigon