Chapter
4A
Pre-Calculus Assignment Guide
Chapter four part A starts a very long journey into trigonometry. We will spend at least 14 weeks
looking at trig functions and their applications but this first chapter examines the building blocks and definitions
that we will use for the next three years. It is critical that you memorize these properties as soon as possible.
As usual, please don’t put them in the short-term memory! Every day we will try and tie these concepts together
and create a firm foundation for future studies. Please ask questions regularly in class or stop by to see me or go
to the Math Resource Center in room C117 for extra help.
1.
4.1
Radian and Degree Measures
p. 255-256
#1-63 odd
2.
p. 256-257
#65-89 odd
3.
p. 255
p. 258
Vocabulary Check: 1-10
#96-101
Angular and Linear Speed Worksheet
4.
Unit Circle Activity
Memorize first Quadrant of the Unit Circle
5.
4.2
Trigonometric functions: the Unit Circle
p. 264
#1-35 odd
6.
4.2
Trigonometric functions: the Unit Circle
p. 264-265
#37-59 odd
4.3
Right Triangle Trigonometry
p. 274
# 3-15, multiples of 3
Right Triangle Trigonometry
p. 274-275
#17-51 odd
7.
4.3
8.
4.3
9.
10.
4.4
Trigonometric Functions of Any Angle
p. 284-286
#1, 5, 9, 13-16, 17, 21, 25, 27, 29-51 odd, 53, 55, 59, 61, 65, 69, 72, 81, 83, 93,
95
Review for Quiz Worksheet
#3
Nov
18-22
Nov
11-15
Chapter Review Sheet
p. 332
Read through Chapter Summary for sections 4.1-4.4. What did you learn?
No School
Veteran’s Day
Nov.
25-29
#53-56 all, 57-65 odd
Exact Values Worksheet
Nov
11-15
11.
p. 275-277
#1
PT Conferences
Ch. 3 Test
#2
#4
UNIT CIRCLE
4.1 Mini Quiz
#5
#9----------------
#6
----------------->
#7
-----------------
Exact Value Quiz
#8
----------------->
No School
No School
No School
#10
4.1-4.3 Quiz
Review
#11
4A Test
Honors Pre-Calculus
Name____________________________
Chapter 4 Day 3 Worksheet: Angular and Linear Speed
Directions for 1 and 2: Use the definition of radian to solve #1 and definition of linear speed to solve #2.

s
r
speed 
distance
time
1.
A highway curve, in the shape of an arc of a circle is .25 miles. The direction of the highway changes 45 degrees
from one end of the curve to the other. Find the radius of the circle in feet that the curve follows.
2.
The radius of the Earth is 4000 miles. What is the linear velocity of a point near the equator? (Hint, the earth
revolves every 24 hours)
Directions for 3 -- 8: Use the use unit analysis to answer the following questions.
3.
To the nearest revolution, how many times will a bicycle wheel measuring 26 inches in diameter turn if it is
ridden for one mile?
4.
If the wheel of the bicycle in the previous problem turns at a constant rate of 2.5 rev/sec, what is its linear speed
in ft/s? How about in mph?
5.
If a wheel with a 16 inch diameter is turning at 12 rev/sec, what is the linear speed of a point on its rim in ft/min?
6.
The crankshaft pulley of a car has a radius of 10.5 cm and turns at 6 rad/sec. What is the linear speed of the
pulley?
7.
Find to the nearest cm/sec the linear speed of a point on the rim of a wheel of radius 24 cm turning at an angular
speed of
8.
17
rad/sec.
12
The linear speed of a point 15.3 cm from the center of a phonograph record is 17 cm/sec. What is the angular
speed of the record in rad/sec?
Bonus: Find the coordinates of the final position of a point P moving counterclockwise in uniform circular motion at


3
rad/sec if P starts at the point ( 5 , 0 ) and moves for 14 seconds.
H Pre-calculus Review for 4.1-4.3 Quiz
As part of assignment #10, do these problems as preparation for the upcoming quiz.
1.
Convert 385 to radians.
2.
Convert
3.
Convert 245 10’ 10” to decimal form.
4.
What quadrant does
5.
Give a coterminal angle for
6.
Find the arc length of a curve that is formed by a 30 angle with a radius of 5 feet.
7.
If a wheel turns at 2 revolutions per second, and the diameter is 4”, find the angular and linear speed of the wheel.
8.
Give the 6 trig values at
9.
Give the exact values of the following:
13
radians to degrees.
11
19
radians lie?
20
5
.
2
11
.
6
a.)
sin
3
2
b.)
cos 
c.)
sin 3
d.)
cos 
e.)
tan 

4

4
3
2
10.
If sin(t) =
2
, find sin(-t).
5
11.
If cos(t) =
2
, find cos(-t).
5
12.
Find the 6 trig functions for  in the triangle below:
8

5
13.
1
3
and Cos 30 =
, find the following values: (don’t cheat and use the values
2
2
in a, b, c, d or e to find the other values, only use the givens!)
If the only thing you know is that Sin 30 =
a.)
tan 30
b.)
csc 30
c.)
cos60
d.)
sin 60
e.)
sec 30
bg
14.
Find sin 40 , csc 4 and cot 45 on your calculator. Make sure you are in the right mode.
15.
Find  if cos  
16.
Find  if tan  .782 in degrees and radians with your calculator.
17.
Sketch the first quadrant of the unit circle. Label the degrees, radians and coordinates.
18.
A forest ranger sights a fire while he is standing in a watch tower 500 feet above the ground. While looking through the
binoculars, her line of sight forms an angle of depression of 10 . How far away is the fire from the base of the tower?
Please sketch a drawing of the situation.
1
and  is in the first quadrant.
2
H-Pre-Calculus
Chapter 4A
Targets
Section 4.1
1.
I can sketch a positive or negative rotation and find co-terminal angles.
Determine the quadrant that each angle lies and find a positive and a negative coterminal angle.
  2 .5
a.
b.
c.
  56
  74
d.
 
11
3
e.
 
13
4
f.
  420o
Determine the quadrant that each angle lies and find it’s supplement and complement (if possible).
g.
2.
3.
 
5
6
h.
 
5
4
i.
 3
I can convert between degrees/radians and between D°M’S’’/decimal degree.
Convert the following angle measures from degrees to radians.
a.
153o
b.
521.5o
c.
-71o
Convert the following angle measures from radians to degrees.
5
12
d.
e.
7
5
f.
5.5
Convert the following angle measures to D°M’S’’
g.
153.658o
h.
i.
-71.123o
521.5o
I can define radians in terms of arc length and radius and solve for unknowns.
Find the length of the arc intercepted by a central angle with the given radius.
a.
4.
 
5
6
r  3 inches
b.
  173o
r 12 feet
I can convert between angular and linear speed using unit analysis.
a.
The cylindrical roller on highway roller has a 48 inch diameter and makes .7 revolutions per
second. Find the angular speed of the roller in radians per second and find the linear speed of the roller.
b.
The tire on a car has a radius of 16 inches and is spinning at a rate of 4 revolutions per second.
Find the angular speed of the roller in radians per second and find the linear speed in mph.
Section 4.2
5.
I can define and evaluate the six trig functions in terms of x and y on the unit circle.
Evaluate the six trigonometric functions of the real number.
t  23
t  34
a.
b.
6.
c.
t
11
6
I can identify which trig functions are odd and which are even and, given a trig value at some
angle “t,” I can evaluate related trig functions at “-t.”
a.
Identify the trig functions are odd and which are even. Use a specific example of each function to verify your
identification.
b.
If cot t  3 , then tan  t = ?
c.

 
If sin  t   7 , then sin  t  = ?
7.
I can identify the “important” angles (degree and radian) and the (x, y) coordinate on the unit
circle.
a.
Draw a unit circle and complete the important points – degree, radian, and (x, y) points.
b.
Evaluate exactly cos

3
 tan
2
5
 sin
.
3
6
Section 4.3
8.
I can use a triangle and 2 given sides to evaluate the six trig functions.
Find the exact values of the six trigonometric functions of the angle θ.
a.
b.
15
9
11
θ
θ
6
9.
I can simplify and evaluate trig expressions using the fundamental trigonometric identities (6
complementary, 6 reciprocal, 2 quotient identities and 3 Pythagorean identities).
a.
Given
cos( ) 
b.
Given
tan( ) 
2
7
9
4
Given
sec( ) 
19
6
c.
10.
in a right triangle, determine the other five trig functions.
in a right triangle, determine the other five trig functions.
in a right triangle, find sin  , cos  an cos( 90
o
 )
I can use inverse trig functions to find Ө in both radians and degrees by memory or with a
calculator.
Evaluate exact values for θ when possible, otherwise use a calculator. Give both the degree & radian measure. Assume θ is
in the first quadrant.
11.
a.
sin( ) 
3
2
b.
cos( ) 
1
2
c.
tan( ) 
3
3
d.
sin( ) 
2
3
e.
cos( ) 
1
4
f.
tan( ) 
17
2
I can evaluate trig functions at a given angle by memory or with a calculator.
Find exact values for θ when possible, otherwise use a calculator. Assume θ is in the first quadrant.

a.
csc(120o )
b.
sec 12o51' 45 "
d.
csc(68o35 ")
e.
sec  73 

c.
tan  56 
f.
tan 12.5
12.
I can solve real world trig problems with sine, cosine and tangent
a.
A person standing 100 meters from the base of a vertical tower places a transit on the ground and determines the
angle of elevation to the top of the tower is 4.749o. Determine the height of the tower.
b.
A building has a row of lights around the sides of the building 30 feet below the top of the building. A marker on
the street that approaches the building notes that the angle of elevation to the top of the building is 10o and the angle
of elevation to the row of lights is 6o. How far from the building is the marker on the street and how tall is the
building?
c.
The sonar of a navy cruiser detects a submarine that is 7000 feet from the cruiser. The angle between the water level
and the submarine is 25o. How deep is the submarine?
Section 4.4:
13.
I can determine the six trig functions exact value given a point on the terminal side of an angle in
standard position.
a.
b.
c.
14.
I can evaluate trig values given one value and other information.
a.
Given sin   34 and cos   0 , evaluate tan  and sec  .
b.
Given tan   74 and sec   0 , evaluate sin  and cos  .
c.
Given sin   53 and θ is in Quadrant II, evaluate cos  and sec  .
d.
Given tan   35 and θ is in Quadrant IV, evaluate sin  and sec  .
e.
15.
Given the point ( 5, -7 ) on the terminal side of an angle, determine the six trig functions.
Given the point ( -6, -4 ) on the terminal side of an angle, determine the six trig functions.
Given the point ( -3, 8 ) on the terminal side of an angle, determine the six trig functions.
Find Ө if
cos  .2586 and 0    360
(remember, there should be two answers!)
I can find and sketch the reference angle of a rotation.
Find the reference angle of each of the following.
a.
16.
θ = 315o b.
θ = 16.7 c.
θ = -30.2
d.
19
4
I can use trig identities to find other trig values given information about one trig value.
Use the Pythagorean identities to evaluate each of the following.
a.
Given sin   34 and cos   0 , evaluate tan  and sec  .
b.
c.
d.
tan   74 and sec   0 , evaluate sin  and cos  .
Given sin   53 and θ is in Quadrant II, evaluate cos  and sec  .
Given tan   35 and θ is in Quadrant IV, evaluate sin  and sec  .
Given
H-Pre-Calculus
Chapter 4A Target Answers
1a.
1b.
1c.
1d.
1e.
1f.
1g.
1h.
1i.
2a.
2b.
2c.
2d.
2e.
2f.
2g.
2h.
2j.
3a.
3b.
4a.
7
6
15
4
III ,
IV ,
, 176 
, 4
II , 2.5  2 , 2.5  2
IV , 53 , 3
II ,
3
4
,
5
4
I , 60o ,  300o
II , sup 6
III
II , sup :   3
2.670
9.102
-1.239
128.5710
4320
-315.1270
153039’28.8”
521030’0”
-71o7’22.8”
s = 7.854 in
s = 36.233 ft.
  4.398
sin(θ)
9 117
117
cos(θ)
2 26
15
6 117
117
tan(θ)
11 26
52
3
2
cot(θ)
2 26
11
2
3
sec(θ)
15 26
52
117
6
csc(θ)
15
11
117
9
sin(θ)
cos(θ)
rad
sec
  25.133
a
b.
3 5
7
2
7
9 97
97
4 97
97
9
4
tan(θ)
3 5
2
cot(θ)
2 5
15
7
2
4
9
7 5
15
97
9
sec(θ)
csc(θ)
rad
sec
mi
hr

10b.
60o ,

 3
3
10c.
30o ,

1
 3
10d.
28.126o , 0.491
2
 2
2 3
3
2
75.522o , 1.318
2 3
3
 2
10e.
10f.
83.290o , 1.454
11a.
2 3
3
5c.
sin(t)
3
2
 2
2
1
2
cos(t)
1
2
 2
2
3
2
tan(t)
 3
1
cot(t)
 3
3
sec(t)
csc(t)
6a.
even:
Odd:
6b.
6c.
7a.
-3
cosine, secant
sine, tangent,
cotangent, cosecant

See your unit circle
1 3
a.
b.
c.
sin(θ)
7 74
74
2 13
13
8 73
73
cos(θ)
tan(θ)
5 74
74
7
5
3 73
73
8
3
cot(θ)
5
7
3 13
13
2
3
3
2
sec(θ)
74
5
 13
3
 73
3
csc(θ)
 74
7
 13
2
73
8
14a.
14b.
14d.
cos(90   )  51913
60o ,
5b.
11b.
11c.
11d.
11e.
11f.
3
3
6
1.0257
 3
3
1.074
2
0.066
8.308 meters
421.214 feet, 4.271 feet
2958.328 feet
13.
97
4
sin( )  51913
cos( )  196
10a.
5a.
12a.
12b.
12c.
14c.
in
sec
9c.
linear speed  22.848
7b.
8b.
11
15
9.
linear speed  105.558
4b.
8a.
tan 
3 7
7
sec 
4 7
7
sin 
7 65
65
cos 
4 65
65
cos  
sec 
4
5
5
4
sin 
5 34
34
sec 
34
3
14e.
105o or 285o
15a.
15b.
15c.
15d.
45o
0.992 radians
1.216 radians
16a.
16b.
16c.
16d.
see 14a
see 14b
see 14c
see 14d

4
radians
,
,
3
8