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