Do Now quick Summary Sheet
Quiz Due at 2:20 pm
 As a freshman, you invest $3,000 in a bank account
that yields 5.5% interested compounded quarterly. 5
years at Hyde how much $ will you have?
 HYPER MATH
UNIT 5 TRIGONOMETRY
Class One:
Degrees Radians
 Radian Unit Circle
 Do Now
 Convert to Degrees Measure:
 π/4=
3π/2=
π/6 =
 Convert to Radian Measure {keep π}
 330 =
285=
92 =
 Homework: page 352 – 353 #’s35,41,49,55,63,67, 77*
To convert from radians to degrees, multiply the angle by 180/π
To convert from degrees to radians, multiply the angle by π/180
UNIT CIRCLE
Unit Circle Degree --> Radian
CLASS TWO: TUESDAY JAN 25
COTERMINAL ANGLES
DEGREES – MINUTES - SECONDS
ARC LENGTHS
Do
 IF
Now:
f(x) = 2x2 + 2x - 3
 Find
 Page

the Roots and Vertex
352-53 #47 , #57
Homework
 Page
353
77, 79, 91 – 98 all
#99
COTERMINAL ANGLES

Coterminal Angles have the same
 INITIAL
SIDE
 TERMINAL SIDE
 Example 2 page 343
For example
30°, –330° and 390°
are all Coterminal.
DEGREES – MINUTES – SECONDS

Page 344 example 4/ Example 5
60 minutes / degree
 60 seconds / minute
 3600 seconds / degree


Convert 45.65 to deg-min-sec

Convert 65° 35’ 22” to degree decimal
ARC LENGTH
Arc Length (s) = α * r
 Θ  degrees
 α  Radian
 Arc Length (s) = α * r
 Arc Length (s) = Θ *{π/180} * r


Example 9 Page 349

Find the distance a mountain bike wheel covers after
(1) revolution? {mountain bike tires are typically 26” in
diameter}

Class Three
Arc Lengths
Linear Velocity
Angular Velocity
{Distance / Area }
Do Now
◦ Find and graph the linear equation that goes through
◦ the points (3, 5) and ( 5, 10)
◦ Page 353 #91 Find the Arc Length if
 α = π/4 and the radius is 12 feet
Homework
 Page 349

Examples 9 and 10
◦ Page 354 #, 99, 100, 103, 104, 113, 114,
◦ 105 – 109
Linear Velocity
Angular Velocity
Linear Velocity
= distance / time
= meters /sec
= ft / sec
V=s/t
Angular Velocity
= Angle / time
= Radians /sec
= Degrees / sec
ω=α/t
Example 11
Example 12
 In Class


The average radius of the Earth, or the distance from the center to surface is 6,371
km, or 3,959 miles.
But wait, the answer is actually a little more complicated than that. As you
probably know, the Earth is rotating on its axis, completing one full revolution in
just less than 24 hours. This relatively rapid rotation causes the Earth’s poles to
flatten, and our planet bulges at the equator. Instead of a perfect sphere, the Earth
is a flatted sphere. This means that the distance from the center to the equator is
further than the distance from the center to the Earth’s poles. The equatorial
radius of the Earth is 6,378.1 km, and the polar radius of the Earth is 6,356.8 km.
Subtract those two numbers and you get 21.3 km. In other words, points on the
equator are actually 21.3 km further from the center of the Earth than the poles.
 Find the distance from Rio de Janeiro [22º 54' 10" S]
 to Miami Florida [25° 46' 26" N ] using the average
radius of Earth
 In Class Homework
 Page 349
Examples 9 and 10
 Page 354 #, 102, 105 – 109 , 110, 111,
 HONORS #’s
 Page 354 #, 99, 100, 103, 104, 113, 114,
Do NOW
What is the length of the
crust of 2 slices from a 20”
pizza cut into 10 EQUAL
pieces?
What is the AREA of the 2
pieces?
DO NOW
page 356 pop quiz
# 1 – 7 all
 In Class WORK TOGETHER TO SOLVE ALL THE
Homework PROBLEMS
 Page 349
Examples 9 and 10
 Page 354 #, 102, 105 – 109 , 110, 111,
 HONORS #’s 115, 116
 Page 354 #, 99, 100, 103, 104, 113, 114,
 TUESDAY TEST on Page 353 any of the problems
Day Five Word Problems
Angular and Linear Velocity
Basic SIN and COS
 Do Now:
 Find the COS (α)of α = 9π/2 =__________
 Convert 600 degrees into Radians and find the COS of the
radian measure. =________________
 Find the ARC Length if α = π/4 and r = 12ft =_______
 Solve for x if 3x = 7
x = _____________
 Homework:
 Reference Angle – page 361 Example 4
 Fundamental Identity – page 36 Example 7
 Page 366 For Thought 1 – 10 ALL
Day Five Word Problems Feb 3 2011
Angular and Linear Velocity







DO NOW
Page 354 # 106
Linear Velocity
In Class
Page 354 # 108
Angular Velocity
Page 354 # 110
Linear Velocity with trig
Page 354 # 113
Area of a circle sector
Page 356 Linking Concepts 20 meter Ferris wheel






ac
Reference Angle – page 361 Example 4
Fundamental Identity – page 364 Example 7
Homework CHANGE pg 354 – 355 101 – 113 ODD
Summary Sheet for Quiz
Conversion
Arc Lengths
DO NOW: Find the radius of a circle whose ARC Length is 10
Feet and the central angle is π/12 radians=
 Last Nights Homework


CHANGE pg 354 – 355 101 – 113 ODD
115 and 116 ALL or NOTHING
 Summary Sheet for Quiz

Conversion
Arc Lengths
 IN CLASS TODAY (Friday) Graphing SIN and COS
Do
Now:
• Find the SIN and COS of the
following to four decimal places:
• Example 1 page 357
•
•
•
•
•
•
Θ=33°
Θ=123°
Θ=333°
α = 3π
α = 3π/2
α = 4π/3
Sin = ____ Cos = ____
Sin = ____ Cos = ____
Sin = ____ Cos = ____
SIN = ___ COS = ___
SIN = ___ COS = ___
SIN = ___ COS = ___
In class – Homework
Know the 1st quadrant SIN COS for Primary Angles
0 – 30 – 45 – 60 – 90 0 - π /6- π /4 - π /3 - π /2
MAKE YOUR Degree Wheel
Page 361
Example 4 Reference Angle
Page 366
For Thought 1 – 7
Page 366 – 367
#’s 7 – 15 ODD 29 – 35 ODD
 IN
CLASS  Homework
 Motion of a spring
• Example 8 Page 365
 Word
Problems
• Page 367 #’s 95 – 100
 Pop
Quiz page 368 1 – 8 ALL
Day Eight: Graphing
Amplitude
Period
Shift
{Phase Shift}




Do Now: On your Calculator - graph {in Radians}
Y = SIN(X)
Y = COS (X)
Y = COS (X – π/2)
 IN CLASS:
 Graph Y = 4 SIN (X)
 Graph Y = 4 SIN(2X)
 Graph Y = 4 SIN (X) +3
 Fundamental SIN Equation  f(x) = A SIN{Bx} + D
Day Eight: Graphing
 Trigonometry - Graphing
 Plot the equations for a SIN or COS function
f(x) = D + A SIN (B {x – C})
 a)



D = shift on the “Y” axis
= {MAX + MIN} /2
A = Amplitude
= {MAX – MIN} /2
B finds the period of the cycle = 2π / B



If B = 1 then the “normal” period is 2π
(a circles circumference)
C = shift on the “X” axis
Homework: {Page 381}
#’s 1 – 4 ALL
GRAPH - #’s 5, 6, 15, 16, 21, 23
 Graph the equation f(α) = Y = 2 + 4 * SIN ({1/4} α)
DAY NINE MORE SIN – COS GRAPHS

Physics Oscillations - Simple Harmonic Motion
= SINE WAVES
f(x) = D + A SIN (B {x – C})

Simple Haronic Motion EQUATIONS
 X(t)
= A Sin (ωt + ф)
 F(x) = -kx
 Homework
Pg 383 77-85 ODD
DAY TEN DO NOW:
If the frequency of a sound wave (SIN wave) is
40,000 cycles per second (Hz).
 a) What is the period?


b) If the Amplitude is 5.5 what is the SIN
equation that governs the sound wave?
GRAPHING SIN & COS
Homework:
 Page 384 – 385 #86,87,91,93

Day 11 Review
 Do Now: #1 CLEAN THE ROOM
 #2 If a company experiences its maximum sales
($40,000) in December and its lowest sales in June
($10,000), write the trigonometric equation if
December is month zero and t= the # of months after
December.
Day 11 Review
Angles
Velocities
 What is the reference angle for  What is the linear velocity of
120 degrees? =
 What is the exact value for Sin
(3π/4) =
 What is the value of:
 Sin2(37π/42) + Cos2(37π/42) =
the second hand of the clock
in room one if the second
hand has a length of 3” in
ft/sec =
 What is the angular velocity
of the minute hand of the
clock in room one if the
minute hand has a length of
5” in ft/sec =
Day 12 TEST
Homework
 Basic Trigonometric Functions
 Tangent
 Cotangent
 Secant
 Cosecant
 Page 396
 #’s 1 – 6 all
 Page 397
 #’s:
3,5,7,11,15,29, 31,33,35
 Honors #51
Day 13 Group B and E
Group B
Group E
 Linear






- Quadratic
Reference – Coterminal
Angular – Linear Velocities
Graph SIN – COS
f(x) = D+A*SIN(Bx)
 Homework :
 Page382 #’s 41 – 47 ODD

Linear - Quadratic
Reference – Coterminal
Angular – Linear Velocities
 Graph SIN – COS –
 Graph TANGENT
 Homework
 Page 386
 #’s 1-5 ALL
 Page 397
 #’s 51,52,57,58, 63, 64
Day 14A (Feb 16)Group B and E
Group B Do Now
Graph f(x) = 5 + 2Sin (2 {x})
 Day 14 Graph SIN – COS
 f(x) = D + A*SIN(B*x)
 In-Class /Homework
 Page 382 #’s 55, 59, 60, 62
Group E Do Now
Graph f(x) = 5 + Tan(2 {x + π/2})



Linear
- Quadratic
Reference – Coterminal
Angular – Linear Velocities
 Graph SIN – COS –
 Graph TANGENT
 Recognize COT – SEC - CSC
 In-Class /Homework
 Page 392 Examples 4, 5, 6,
 Page 396 Gallery
 Page 398 #’s 83 – 92 Honors 97
Day 14B (Feb 17)Group T= Travel Lane and F = Fast Lane
Group F Do Now
Group T Do Now
Graph f(x) = 3.5 + Tan(1/2 {x})
Graph f(x) = 3.5 + 5*Sin (1/2 {x})



Linear
- Quadratic
Reference – Coterminal
Angular – Linear Velocities




Graph SIN – COS –
Graph TANGENT
Recognize COT – SEC - CSC
In-Class /Homework



Page 392 Examples 4, 5, 6,
Page 396 Gallery
Page 398 #’s 83 – 92 Honors 97
 Graph COT – SEC – CSC
 Find:
-1
-1
-1
 SIN – COS – TAN
 ArcSIN – ArcCOS = ArcTAN
 In-Class /Homework
 Page 403 example 5, 6, 7, 8
 Page 408 #’s 1 – 35 ODD<3
 Linear - Quadratic
 Reference
– Coterminal
 Arc Length
 s=α r
 Angular – Linear Velocities page 350
 ω =α/t
 v =s/t = 2πr/t = αr/t
 v = r*ω
 In-Class /Homework
 Page 349 - 351 Examples 9 - 10 - 11
 Page 354- 355 #’s 103, 104. 107, 108,
111
Day 15 Feb 18
Group F Do Now







Linear
- Quadratic
Reference – Coterminal
Angular – Linear Velocities
Graph SIN – COS –
Graph TANGENT
Graph COT – SEC – CSC
Find:



SIN-1 – COS -1 – TAN -1
ArcSIN – ArcCOS = ArcTAN
In-Class /Homework


Page 403 example 5, 6, 7, 8
Page 408 #’s 1 – 35 ODD
 Page 420 43 – 49 ODD
 NEW STUFF USING TRIG!!!
Group T Do Now


Linear
- Quadratic
Reference – Coterminal


Graph SIN – COS
f(x) = D + A*SIN(B*x)

Arc Length


s=α r
Angular – Linear Velocities page 350
ω =α/t
v =s/t = 2πr/t = αr/t
v = r*ω
In-Class /Homework

Page 349 - 351 Examples 9 - 10 - 11

Page 354- 355 #’s 103, 104. 107, 108, 111




 MONDAY
 Graph TANGENT page 389-390
 f(x) = D + A*Tan (Bx)

P = π/B (NOT 2 π/B )
 In-Class /Homework


Page 389 example 2 391 gallery
Page 397#’s 51, 52, 57, 58, 63, 64
Monday Presidents Day
Group F:
Do Now: Which Presidents
does Presidents Day
HONOR?
Group T RETAKE TEST
 Non Right Triangles
 Homework
 Page 510 & 520
 MONDAY
 Graph TANGENT page
 #’s 5 – 19 ODD
LAW of COSINE
c2 =
a2 + b2 – 2ab*COS C
b2 =
a2 + c2 – 2ac*COS B
a2 =
c2 + b2 – 2cb*COS A
LAW of SINE
SIN (<A) / a = SIN (<B) / b = SIN (<C) / c
where :
a, b, and c are SIDES OPPOSITE
Angles <A, <B, and <C
389-390
 f(x) = D + A*Tan (Bx)
 P = π/B (NOT 2 π/B )
 In-Class /Homework
 Page 389 example 2 391
gallery
 Page 397#’s 51, 52, 57, 58, 63,
64
Do Now:
Find all 3 angles and 3 Sides
If Side a = 4 b= 7 c=?
<A = 55 <B= ? <C =?
Group T MALI Willie and
TUESDAY Feb 22
 Non Right Triangles
 Homework CHECK
 Page 510 & 520 #’s 5 – 19
ODD
 LAW of SINE



SIN (<A) / a = SIN (<B) / b = SIN (<C) / c
where :a, b, and c are
SIDES OPPOSITE Angles <A, <B, and <C
 In Class Page 511 #31 – 39 ODD
GABI RETAKE TEST
 Homework
 TUESDAY IN CLASS
 Graph TANGENT page
389-390
 f(x) = D + A*Tan (Bx)
 P = π/B (NOT 2 π/B )
LAW of COSINE
c2 =
a2 + b2 – 2ab*COS C
b2 =
a2 + c2 – 2ac*COS B
a2 =
c2 + b2 – 2cb*COS A
NEW Heron’ s Rule :
Area = √{s* (s-a) (s-b)(s-c)}
Where s = ½ * ( a + b + c)
 In-Class /Homework
 Page 389 example 2 391
gallery
 Page 397#’s 51, 52, 57, 58, 63,
64
Day 16 Group T and F
Group F




Linear
- Quadratic
Reference – Coterminal
Angular – Linear Velocities

Graph SIN – COS –
Graph TANGENT
Recognize COT – SEC – CSC

Find:



SIN-1 – COS -1 – TAN -1
ArcSIN – ArcCOS = ArcTAN
 MORE USING TRIG
Group T





Linear
- Quadratic
Reference – Coterminal
Angular – Linear Velocities
Graph SIN – COS
f(x) = D + A*SIN(B*x)
 Graph TANGENT page 389-390
 f(x) = D + A*Tan (Bx)
 P = π/B (NOT 2 π/B )
 In-Class /Homework
 Page 389 example 2 391 gallery
 Page 397#’s 51, 52, 57, 58, 63, 64
 Page 387 Recognize
 COT (Θ) – SEC (Θ) – CSC (Θ)
 COT (Θ) = 1 / TAN (Θ)
 SEC (Θ) = 1/ COS (Θ)
 CSC(Θ) = 1/ SIN(Θ)
Fast Lane - Vectors
Homework
– Summary Sheet

Travel Lane – SOH CAH TOA
FINDING THE SIDES
Homework
– Summary Sheet
 Given a Right Triangle with
one angle and one side
 Find the missing angles and




missing side
A2 + B2 = C2  Adj2 + Opp2 = Hyp2
SIN θ = Opp/ Hyp
SOH
COS θ = Adj/ Hyp
CAH
TAN θ = Opp/ Adj
TOA
Hyp
Opp
Θ
Adj
Finding the ANGLES
 Given a right triangle three
sides
 Sin 30 = ½
 ARCSIN (1/2) = 30 Degrees
 Find the missing angles
 ARCSIN (Opp / Hyp ) = θ
 Sin 45 = .7071
 ARCCOS (Adj / Hyp ) = θ
 ARCSIN (o.7071) = 45 degrees
 ARCTAN (Opp / Adj ) = θ
B
c
a
A
C
b
C= 90
c = 10
C= 90
c = __
A = 40
a = ___
A = 30
a = 10
B = ___
b = ___
B = ___
b = ___
C= 90
c = 10
A = ___
B = ___
a = 6.4278 b = ___
C= 90
c = 20
A = ___ B = ___
a = 10
b = ___