Students,
Take out your calendar and your homework. Take out your spiral
notebook and Complete the DNA. Use your notes if
necessary.
1) On a blank unit circle fill
in the degree measures.
2) On the blank unit circle fill
in the radian measures.
3) On the blank unit circle fill
in the coordinates.
Unit Circle
 1 3
 2, 2 



(–1, 0)

3 1
 2 , 2 



2
 2 ,

90°
2
3 3 120°
5 4 135°
6 150°

2 2
 2 , 2 



3,1

 2 2


y (0, 1)
180°

2

60° 3
1 3
2, 2 


 2 2
 2 , 2 



4
45°

30° 6
 3 1
 2 ,2


x
0° 0
360° 2 (1, 0)
330°
11
315°
 3 1
7 210°
6
6  2 , 2 
225°


7
5
240° 300°
2  4 4
5 4  2 ,  2 

2 
2 
 2
3 270° 32 3
 1
3

,

 2
2 

(0, –1)
1
3
,

2
2 

Opp side of θ

Adj side of θ
sohcahtoa
opp
sin  
hyp
adj
cos  
hyp
opp
tan  
adj
hyp
csc  
opp
hyp
sec  
adj
adj
cot  
opp
choshacao

1
sin 30  sin 
6 2

3
cos 30  cos 
6
2

3
tan 30  tan 
6
3
3
sin 60  sin 
3
2
 1
cos 60  cos 
3 2
tan 60  tan
3
 3
2
3
1
60


1
60
30
30
2
45
2
45
2

2
sin 45  sin 
4
2

2
cos 45  cos 
4
2
tan 45  tan

4
1
1) A biologist wants to know the width W of a river in
order to properly set instruments for studying the
pollutants in the water. From point A, the biologist
walks downstream 70 feet and sights to point C. From
this sighting, it is determined that θ = 54°. How wide is
the river?
2) A 12–meter flagpole casts a 12–meter shadow, as
shown in the figure. Find θ, the angle of elevation to
the sun.
2
1) Evaluate the six trig functions of t  
.
3
2) Evaluate the following without a calculator.
9
a) cos
3
 11 
b) sin  

 2 
2
3) If tan t   , find tan  t .
3
4) Use a calculator to evaluate.
5
a) sin
7
b) csc 2
Use a calculator to find the trig ratios.
1) tan 37
2) tan( 3.22)
  6 
3) cos

 11 
4) tan  56
 4 
5) csc

 11 
6) sec(11)
  2 
7) cot

 7 
Linear and Angular Speed
arc length s
Linear speed 

time
t
central angle 
angular speed 

time
t
2) The circular blade on a saw rotates at 2400
revolutions per minute.
a)Find the angular speed in radians per second.
b)The blade has a radius of 4 inches. Find the linear
speed of a blade tip in inches per second.
1) Convert 60 from degrees to radians.
2) Find the supplement of an angle
5
measuring  
.
7
3) On a circle with a radius of 9
inches, find the length of the arc
intercepte d by a central angle of 140.