Investigation 8B bl 2.notebook
December 12, 2012
OLD
p690
FRESH
p715
Dec 5­7:17 AM
Dec 7­1:06 PM
Solutions to 8A
Reflections
Dec 7­1:08 PM
Dec 7­1:22 PM
A simultaneous look...
OLD
p691
FRESH
p715
90
180
270
0 30 60 90 120 150 180 210 240 270 300 330 360 (even or odd)
Dec 5­7:19 AM
Dec 5­7:14 AM
1
Investigation 8B bl 2.notebook
December 12, 2012
cos x at x = 0
cos x at x = 90
cos x at x = 180
cos x at x =270
The cosine
cosine x at x = 0
Dec 7­1:38 PM
Dec 5­7:21 AM
p719
What will the
graph look like?
Dec 5­7:23 AM
CHECKLIST...
Sine....check
Cosine...check
What's Next?????
TANGENT
How have we defined the tangent ratio?
Dec 5­7:23 AM
Dec 5­7:23 AM
A few questions for you before we begin...
.
1.) When are fractions...
a.) Undefined?
b.) Zero?
c.) One
2.) 1/large positive number ≈
3.) 1/large negative number ≈
4.) 1/small positive number ≈
5.) 1/small negative number ≈
Dec 5­7:26 AM
2
Investigation 8B bl 2.notebook
December 12, 2012
The ratio function...
May 10­10:07 AM
May 10­10:16 AM
The ratio function...
Dec 5­7:29 AM
Dec 5­7:29 AM
May 10­8:36 AM
May 10­7:33 AM
3
Investigation 8B bl 2.notebook
December 12, 2012
Why is it called the tangent function?
Geometry????
Dec 5­7:31 AM
Dec 5­7:30 AM
p720 (3,8-13,16)
p725 (3,4,7a,c,9-12,15)
Quiz 8A and 8B Wednesday or Thursday
Dec 5­7:32 AM
May 11­7:12 AM
May 11­7:12 AM
May 11­7:12 AM
4
Investigation 8B bl 2.notebook
December 12, 2012
May 11­7:13 AM
May 11­7:13 AM
May 11­7:13 AM
May 11­7:13 AM
HW solutions
p720
Dec 9­10:56 AM
Dec 9­11:08 AM
5
Investigation 8B bl 2.notebook
December 12, 2012
WARM UP...
May 11­7:14 AM
Dec 9­2:10 PM
Read top of page 727 and complete FYTD...
Given the two sides of an angle of
a triangle what is the area of the
triangle?
May 11­9:54 AM
Dec 6­6:37 AM
A B
X
y
Use your solution and the fact that cos x = sin (90 ­ x ) to come up with an expression for cos (A+B)
1. Using our new definition for area of a triangle, write a formula for the area of the largest triangle 2. Write a formula for the two smaller triangle
3. How are they related.
4. Work with your equation to get an expression for the sin(A + B)
Dec 9­12:05 PM
Dec 9­12:19 PM
6
Investigation 8B bl 2.notebook
December 12, 2012
Cos (A+B)
Dec 6­7:17 AM
Dec 6­6:57 AM
Find the sin(75) (without a calculator)
p733
Find the cos(105)
Dec 9­8:34 PM
Dec 6­7:09 AM
If
Sin (A+B)=SinACosB + CosASinB
then Sin (2A) =
Dec 6­7:10 AM
Dec 6­7:11 AM
7
Investigation 8B bl 2.notebook
December 12, 2012
Homework
p 732(1,2,8-11,17)
Read Proof 1 p 728,29
Proof 2 p 731
p734(1-8)
Review for Thursday's Quiz
p 713(1-8)
Dec 6­7:12 AM
Dec 6­8:58 AM
Dec 6­6:42 PM
Dec 6­6:42 PM
Dec 6­6:43 PM
Dec 6­6:43 PM
8
Investigation 8B bl 2.notebook
December 12, 2012
Dec 6­6:43 PM
May 14­7:31 AM
Dec 6­6:43 PM
May 14­7:32 AM
WARM UP
1.) Provide the other two trig values if tanθ = 8/15 and sinθ<0.
What is the value of θ? Did you need this in order to answer the
first question? Why or why not?
2.) Were you able to derive each of the following last night?
Cos(2A)
Sin(2A)
Cos (A - B)
Sin(A - B)
If not please try it now.
Hey....how about Tan(A+B)?
May 14­7:32 AM
Dec 6­6:59 PM
9
Investigation 8B bl 2.notebook
December 12, 2012
Always...sometimes...never
Sometimes solutions should be given as a
general rule.
s
s
a
a
s
s
7.) sinθ= ­ sin(­θ)
a
8.) tanθ = tan(180o-θ)
s
n
9.) 1 = sinθ
cosθ
tanθ
a
10.) sinθ =- cos(270o - θ)
Dec 6­7:06 PM
Dec 6­6:46 PM
p735
Dec 6­6:59 PM
May 14­7:30 AM
Homework
p737 (1-3)
p739 #12, 13
p 744 #2
Dec 9­1:39 PM
Dec 9­1:54 PM
10
Attachments
Compound_Angle_Proof.ppt