Date
Assigned
9/16
9/19
9/20
9/21
9/22
9/23
9/26
9/27
9/28
9/29
9/30
10/3
10/4
10/5
Assignments for Test #1.3– Pre-Calculus GT/H – 4.1 – 4.4 Johnston/Noonan
September 16 to October 5, 2011
* Memory Quizzes may be taken at any time beyond 9/20/2011
Notes/Activity/Objectives
Homework
Sect 4.1: Locating Angles on a circle in
the coordinate plane in Degrees and Trig
Vocab
Notes Pg 2
Paper Plate Activity for the Unit Circle
Check Homework
p.291 #31 – 46 all
Continue Paper Plate Activity to include
30-60-90 and 45-45-90 right triangles
place coordinates on the plate
Sect 4.1 – Angles in the Plane – Radians –
Notes Page 3
Sect 4.4 – Reference Angles - Notes Page
4
Pg 299: 5 - 21 odd
Quiz #5 – Angles (Degree and Radian)
Sect 4.1: Arc Length , Area of a Sector
Notes Pages 4 and 5
Sect 4.1 Linear & Angular Velocity
Notes Pages 5 and 6
Sect 4.3: Right Triangle Trigonometry
Notes page 6
Quiz #6: Arc Length, Area of a sector,
Linear and Angular Velocity
Sect 4.2: Unit Circle – Discuss period and
even and odd characteristics Notes Page 7
Sect 4.3: Evaluate Trig Functions with a
Calculator using Basic Trig Identities
(introduce cofunctions p. 374)
Notes page 7
Sect 4.4: Trig Functions of any Value
determine trig functions of any angles (in
terms of x, y, and r), signs of trig values in
quads +/- Notes page 8
Quiz #7 – Unit Circle (fill in the blanks),
odd/even functions, 4.4 more calculator
trig , finding solutions to equations using
unit circle Notes page 8
More Practice/ review
pp.365 – 366 #3-87 odd
Test #3 – Sections 4.1 – 4.4 (Intro to Trig)
p. 292: 79 – 93 odd
Piecewise Project Due
Complete Paper Plate Activity
p. 290: 7 – 23, 43 – 77 odd
p. 319: 37 – 44 (reference angles)
WS – Linear and Angular Velocity
Pg. 292: 95 – 100, 106, 107
p. 308: 1 – 4 all, 9 – 15 odd, 17 – 20 all
p. 299: 1, 3, 23 – 41 odd
p. 300: 43 – 52
p. 309: 27 – 35, 43 – 45, 53-63 odd, 73-82
Pg. 319: 1-35 odd, 45 – 63 odd
p. 319: 65 – 86,
Prepare for Test
Print Unit 4
Notes
September 16, 2011
(4.1) Angles in Coordinate Plane – Degrees
Vocabulary:
angle in standard position
initial side
terminal side
vertex
positive angles
negative angles
co-terminal angles
rotation
Draw and label degrees of circle on the axis of the coordinate plane.
State the Quadrant in which the terminal side of the given angle lies and draw the angle in standard position.
1. 187°
2. – 14.3°
3. 245°
4. – 120°
5. 800°
6. 1075°
7. – 460.5°
8. 315°
9. – 912°
10. 13°
11. 537°
12. – 345.14°
Find two angles, one positive and one negative angle, that are co-terminal with the given angle.
13. 74°
14. – 81°
15. 115.3°
Find the complement and supplement for the given angles.
16. 275°
17. – 180°
19. 17.11°
18. – 310°
20. 45.2°
Find the degree measure of the angle for each rotation. Draw the angle in standard position.
5
21. 8 rotation, clockwise
3
22. 5 rotation, counterclockwise
7
23. 9 rotation, counterclockwise
17
24. 4 rotation, clockwise
3
25. 10 rotation, clockwise
5
26. 6 rotation, counterclockwise
Pg 2
Notes
(4.1) Angles in Coordinate Plane – Radians
September 21, 2011
Determine the quadrant in which each angle lies and sketch the angle in standard position.
1.

7
2.

9
3.
6
5
4.
 5
7
5.
17
8
6. 3.7
7.  4.2
r
r
Find the complement and supplement of each angle, if possible.
8.

7
9.
6
5
10. 3
r
11. 1.5
Find the Radian Measure of the angle with the given Degree Measure
12. 330 
13. –72 
14. 145 
15. 765 
Find the Degree Measure of the angle with the given Radian Measure.
18. 
7
2
19.
5
6
20.
r
2
9
21.

12
16. 36 
22. 2
r
17. –120 
23. -1.5
r
III. Find two co-terminal angles for the following. One Positive and One Negative.
24. 135 
25.
11
6
26. 
IV. Determine if the following are co-terminal.
28. -30  , 330 
29.
5 17
,
6
6
30.

4
32 11
,
3
3
27. -50 
31. 50  , 340 
Pg 3
Notes:
September 22, 2011
Reference Angles
Definition of a reference angle:
Find the reference angle
1.
  32
6.

11. 1.4

7
r
 ' and sketch  and  ' in standard position.
2.
  132
7.

12. 2.8
Notes:
9
7
r
3.
  132
8.

 4
5
13.. 4.22
r
4.
  232
9.

 2
7
14. 5.95
r
5.
10.
  200

20
9
15.  1.7
r
September 23, 2011 Arc Length and Area of a Sector
Arc length
Area of a Sector
Find the length of the arc on a circle of radius, r, with central angle,  .
1. r  4; 

6
2. r  3.5; 
3
4
3. r  10;  60
Find the radian measure of the central angle of a circle with radius, r, that intercepts an arc length, s.
4. r = 20, s = 15
5. r= 33 inches, s = 6 inches
Pg 4
Find the area of a sector with radius, r, and central angle,
1. r  5;  120
.
2. r  8.4; 
2
3
Applications
1. Pittsburg, PA is located at 40.5  N while Miami is located at 25.5  N. Assuming the Earth is a perfect sphere, how many
miles apart are the two cities (Earth radius is 4,000 miles).
2. A sprinkler can spray water 75 feet and rotates through an angle of 135  . Find the area of the region that the sprinkler covers.
Notes:
September 26, 2011 Linear and Angular Velocity
Terms and formulas you need to know:
1. Arc Length
2. Area of a Sector
3. Converting Degrees to Radians
4. Revolution
5. Rotation
6. Angular displacement
7. Angular Velocity
8. Linear Velocity
Examples:
1. A CD makes
4
a rotation about its axis. Find the angular displacement in radians
5
2. Find the Angular Velocity in radians per second of a wheel turning 25 revolutions per minute.
3. A sector has an arc length of 16 cm and a central angle measuring .95 radians. Find the radius of the circle and the area of the
sector
4. The wheel of a truck is turning at 6 rps. The wheel is 4 ft in diameter. Find the angular velocity of the wheel in radians per second.
Find the linear velocity.
5. Two pulleys, one 6 inches in diameter and the 2 feet in diameter, are connected by a belt. The larger pulley revolves at the rate of
60 rpm. Find the linear velocity of the belt in feet per minutes. Calculate the angular velocity of the smaller pulley in radians per
minute.
6. A pulley of radius 12 cm turns at 7 rps. What is the linear velocity of the belt driving the pulley in meters per second?
7. A trucker drives 55 mph. Her truck’s tires have a diameter of 26 inche4s. What is the angular velocity of the wheels in revolutions
per second?
Pg 5
Homework/Practice Problems: September 26, 2011 Linear and Angular Velocity
1. An arc is 6.5 cm long and is intercepted by a central angle of 45 degrees. Find the radius of the circle.
2. How many revolutions will a car wheel of diameter 30 inches make as the car travels a distance of one mile?
3. Pittsburg and Miami are on the same meridian. Pittsburg has a latitude of 40.5 degrees north and Miami, 25.5 degrees north. Find
the distance between the two cities. The radius of the earth is 3960 miles.
4. Kim’s bicycle wheel has a 26 inch diameter. To the nearest revolution, how many times will the wheel turn if it is ridden for one
mile? Suppose the wheel turns at a constant rate of 2.5 revolutions per second. What is the linear speed of a point on the tire in feet
per second? What is the speed in miles per hour?
5. A merry-go-round makes 8 revolutions per minute.
a) What is the angular velocity of the merry-go-round in radians per minute?
b) How fast is a horse 12 feet from the center traveling?
c) How fast is a horse 4 feet from the center traveling?
6. A circular gear rotates at the rate of 200 rpm.
a) What is the angular speed of the gear in radians per minute?
b) What is the linear speed of a point on the gear 2 inches from the center in inches per minute?
7. A merry-go-round horse is traveling at 10 feet per second and the merry-go-round is making 6 revolutions per minute. How far is
the horse from the center of the merry-go-round?
Pg. 292: 95 – 100, 106, 107
Notes:
September 27, 2011
hypotenuse
side
opposite

side adjacent to
Right Triangle Trigonometry
sin  
csc  
cos  
sec  
tan  
cot  


Find the exact value of the six trigonometric functions of the angle
1. shown in the figure.

2. Sketch a right triangle corresponding to the trig function,
determine the third side and then find the 5 remaining trig functions.
csc   3
10
24
Pg 6
Notes:
September 28, 2011
Given the coordinate, determine the exact value of the six trig functions.
  5 12 
, 
 13 13 
 15  8 
,

 17 17 
1. 
2. 
Evaluate the trig function using its period and your plate.
3.
cos 7
4. sin
EVEN Trig. functions:
ODD Trig functions:
5. sin
cos(  x)  cos x
sin(  x)   sin x
tan(  x)   tan x
6. If csc t  5 then csc( t )  _______
Notes:
11
4
and
September 29, 2011
 7
2
6. cos
 15
6
sec( x)  sec x
csc(  x)   csc x
cot(  x)   cot x
sin t  ______ then sin( t )  _______
Cofunctions, Calculator Trig.
Cofunction Identities:


sin   u   cos u
2



cos  u   sin u
2



tan   u   cot u
2



csc  u   sec u
2



sec  u   csc u
2

Remember

2


cot   u   tan u
2

 90
Use a calculator to evaluate the trig. function, Round to 4 decimal places.
1. sin
5.

5
2. csc
cos 38
3
7
3. tan 1.28
6. cot 77.5
7.
sin 57.8
4. sec .77
8. csc 29.5
Use the given function values to find the indicated trig values. Draw a triangle or use your plate.
9. cos 30 
1
2
10. tan   3
tan 30 
sec 30 
cos(90  30) 
cot  
sin  
sin 90    
pg 7
Notes:
September 30, 2011
Trig Functions of any angle
Definition of Trig Functions of any angle: Let
a point on the terminal side of

and r 
 be an angle in standard position with ( x, y )
x 2  y 2  0 . Then:
csc 
sin  
sec 
cos  
cot  
tan 
1. Determine the exact value of the 6 trig functions given (4,  7) . Draw a triangle.
State the quadrant(s) in which
2.
 lies.
tan  0
3. sin   0
5. sin   0
cos  0
6.
tan   0
4.
sin  cos
cos  0
7. sin   0 cos   0
Find the values of the 6 trig functions with the given restraints. Draw a triangle.
8. cos  
Find
3
5
9.
 , for 0     , for the following problems.
10. sin  
3
 =_____
2
Notes:
1.
 lies in Quadrant IV
cos  1
cos  0
Put answer in radians.

12. tan   undefined
= ______

= ________
October 3, 2011
cos125
5. sec
11.
csc  2
2.
3
5
csc168
6. cos
3.
 2
7
cot 150
7. tan
13
8
4.
sin 345
8. sin 3.42
r
Find two solutions for the given equations. Use your paper plate.
9. cos  
3
2
10. sin  
 3
2
11. csc    2
12. cot  
3
Pg 8
Trig Degree to Radian Chart - Including Cosine, Sine, and Tangent Values
Ө (Degrees)
Ө (Radians)
Cos Ө
Sin Ө
Tan Ө
0º
30º
45º
60º
90º
120º
135º
150º
180º
210º
225º
240º
270º
300º
315º
330º
360º
Name
Date
Degrees
Radians
Period
sinӨ
cosӨ
tanӨ
Pg 9