PART 2
Date
Topic
Assignment
Friday
9-28
INTRO TO UNIT CIRCLE
Packet p 2
Monday
10-1
Tuesday
10-2
Wednesday
10-3
Thursday
10-4
MORE UNIT CIRCLE PLUS SPECIAL ANGLE
VALUES
QUIZ
# 1 - 12
Packet p 4
Packet p 5
REVIEW GAME
TRIGONOMETRY TEST 1
1
Worksheet on 4.2: The Unit Circle
1. What is the domain and range of the sine and cosine function?
2. Does cos  increase or decrease as
a)  increases from 0 to 90 degrees?
b)  increases from 90 to 180 degrees?
c)  increases from 180 to 270 degrees?
d)  increases from 270 to 360 degrees?
II. Evaluate. Do not use a calculator!
3. Does sin  increase or decrease as
a)  increases from 0 to 90 degrees?
b)  increases from 90 to 180 degrees?
c)  increases from 180 to 270 degrees?
d)  increases from 270 to 360 degrees?
4.
a) sin 180
c) sin 270
o
d) cos 270
o
5.
a) sin (-90)
o
d) cos 360
o
6.
a) sin 
b) cos(-)
c) sin 360
3
c) sin
2
7.
a) cos 2
b) sin(-
b) cos 180
o
o
o
b) cos (-90)
o

)
2

2
3
d) cos()
2
d) cos
c) sin 3
III. Are the following positive, negative or zero? Do not use a calculator!
5
3
8.
a) sin
9.
a) cos 3
10.
a) sin
11.
a) cos -
7
6
2
b) sin
3
3
b) cos
2

4
11
c) sin
6

c) sin 6
5
c) sin
4
b) cos
7
4

3
b) cos
c) sin

6
12.
a) sin 2
b) cos 2
IV. Fill in the blank with < , > , =. Do not use a calculator!
a) sin 40 ___ sin 30
14.
a) sin 310 ___ sin 230
o
b) sin 130
15.
a) sin 169 ___ sin 168
o
b) cos 2
16.
List in order of increasing size: sin 1 , sin 2, sin 3, sin 4
o
o
b) cos 40 ___ cos 30
o
o
o
___ sin 50
____
o
o
cos 1

)
2

3
7
d) cos
4
d) sin
d) cos 4
c) sin 172 ___ sin 8
o
o
c) cos 50 ___ cos -50
o
c) sin 3 ___
17.
List in order of increasing size: cos 1, cos 2, cos 3, cos 4
Find sin  and cos  if your angle goes through the point
18. a) (-3,1)
b)
(1,-2)
c)
19.
There are many values of  for which cos  = 0. Name three of these.
20.
21.
22.
a)
3
4
d) cos (-
c) sin 4
13.
o
d) cos
o
sin (-3)
(-10,-8)
o
Explain the meaning of  = 45o  k  360
What is an equivalent statement if  is expressed in radians instead of in degrees?
Solve each equation for all x . Give your answers in radians.
sin x = 1
b)
cos x = -1
c)
sin x = 0
d) sin x = 2
------------------------------------------------------------------------------------------------------------------------------
2
WS: Special Angle Values #1
Find the quadrant, the reference angle, and the value of each of the following.
Quadrant
Reference Angle
Value
1) cos 45
2) sin225
3) cos90
4) tan120
5) cos
6) sin

3

6
7) sin  60
8) tan

2
3
 11 

 6 
9) sin  
10) cos300
11) sin210
12) tan135
13) cos
3
4
14) sin  120

15) cos180
16) tan
7
6
3
PRE-CALCULUS REVIEW FOR TEST
1)
Find the degree measure of the angle formed by a
2)
An angle measures
o
3)
1
clockwise rotation.
6
2
. Find the degree measure after 1.5 rotations clockwise.
3
Express 210 in radians.
5 
4)
Express
in degrees.
3
5)
The speed of a gear is 5 rpm. Through how many degrees does the gear turn in 1.5 minutes?
6)
Is the sin 200o positive, negative, or zero?
6
7)
Evaluate sin
8)
Compare cos 1
_____
cos (-1)
2
9)
Compare sin 280 o _____sin 300 o
2
10)
Where is the terminal side of the angle after a rotation of
radians?
3
11)
A pottery wheel is 1.8 ft in diameter. How fast does a point on the circumference of the wheel travel if
the wheel makes 150 revolutions per minute? Give your answer is feet per mi.
12)
The terminal side of the angle goes through point (-3,-4). Find the exact value of sin .
13)
Solve for all values of  in radians. sin  = -1.
14)
Find the arc length of the nearest tenth of a centimeter of a circle of radius 7 cm that is intercepted by a
central angle of 85 o .
15)
Does cos  increase or decrease as increases from 90 o to 180 o?
2
16)
Where is the terminal side of the angle after
rotation clockwise?
3
17)
Determine the number of revolutions per minute of a wheel whose angular velocity is 166 rad/s
18)
A sector has a central angle of 60 o and arc length of 6cm. What is its area?
19)
State the quadrant where sin  < 0 and cos  > 0.
20)
A bicycle tire is 70 cm is diameter. If the wheels of the bicycle turn 2.5 times per second, what is the
speed in meters per second of a point on the tire tread?
3
21)
Evaluate sin(
)
2
22)
Find the exact radian measure of the acute angle between any two consecutive hour markings on a clock.
2
23)
The central angle of a sector is a circle is 2.4 radians. The area of the sector is 270 cm . Find the radius
of the circle.
V. Solve each problem. Be sure to write a formula and leave answers in exact form (no decimal
approximations – so no calculator!)
24. The measure of a central angle is 50 and the radius of the circle is 4 inches. Determine the arc length.
25 The length of an arc of a circle is 14 cm. If the radius is 4 cm, what is the measure of the central angle?
26. The length of an arc of a circle is 28.5 inches. If the central angle measures 2.5 radians, what is the
length of the radius of the circle?
27. A 100-degree arc of a circle has a length of 7 cm. What is the radius of the circle?
28. Multiple choice. A central angle in a circle of radius r has a measure of  radians. If the same central
angle were drawn in a circle of radius 2r, its radian measure would be…
A)

2
B)

2r
C) 
D) 2
E) 2r 
4
5