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Precalculus
UNIT 5A ~ REVIEW
For #1 – 2, solve the right triangle.
Round to two decimal places if necessary.
a = 4,   20
1.
2.
b = 17, c = 24

3.
A plane landing at PDX has to descend 1650 ft. over a diagonal distance of 9700 feet.
What is the angle of depression of the plane?
For #4 – 6, use a calculator to find the approximate value, rounded to two decimal places.

4.
sin 40
5.
sec
6.
cot 8
5
 #6 – 7, name the quadrant in which the angle  lies.
For

6.
sin  > 0, cos  < 0
7.

 #8 – 15,

For
find the exact value. Do not use a calculator.

8.
tan
9.
csc 30
4

11.
cot
7 
 6 

14.

3
tan
2

12.
cos

sin


15.

cot  < 0, cos  > 0

5
3
10.
cos

13.
sin 0
For #16 – 19, first fill in the blank with an angle,  , where 0    360 or 0    2 , then
find the exact value without a calculator.
16.
sin 585


17.
sec 750

a) sin 585 = sin ___________

a) sec 750 = sec ___________

b)

18.

cot
4
a) cot

b)
19.
cos
4 = cot __________
a) cos

b)

24.

= cos __________

For #20 – 24, find the remaining trigonometric values.
2 2
1
20.
sin  =
, cos  = 
21.
3
3
22.
22
3
b)


22
3



2
tan  = 9 , 0 <  < 90
 
csc  = 3, cot  < 0


23.

3
3
cos  =  , cot  = 
5
4


sin  = 



15
,  in quadrant IV
17
For #25 – 29, find the exact value of the expression. Do not use a calculator.
1
sin 2 20 
25.
26.
sin 40  csc 40
sec 2 20
 27.
 29.
 28.
sin 63 cos27
tan

5

sin
cos

5

5
4 cos60  3tan 


30.
If sin  = 0.6, find the value of: sin   sin   2   sin   8   sin   20 .
31.

A point on the terminal side of an angle  is (-5, -12). Find sin  .


32.
33.
34.
35.
For what numbers  does sin  = 1?
a) all real numbers

c) odd multiples of
( 90 )
2



b) multiples of  ( 180 )
d) odd multiples of  ( 180 )
 
For what numbers  istan  undefined?
a) all real 
numbers

c) odd multiples of
( 90 )
2


 
b) multiples of  ( 180 )
For what numbers  iscsc  undefined?
a) all real 
numbers

c) odd multiples of
( 90 )
2


 
b) multiples of  ( 180 )
What is the domain ofcos  ?
a) all real 
numbers

c) odd multiples of
( 90 )
2

 
b) multiples of  ( 180 )


d) odd multiples of  ( 180 )
 
d) odd multiples of  ( 180 )
 
d) odd multiples of  ( 180 )
 
 
For #36 – 38, convert to radians. Express the answer in terms of  .
60
105
36.
37.

38.



For #39 – 41, convert to degrees. Round to two decimal places, if necessary.

8
39.
40.
41.
6
5



7
4

42.
The following is an angle given in radians. Convert to degrees. Round to two decimal
places if necessary.
9.95
43.
The length of an arc, s, is 10 ft. The radius is 2/3 ft. What is the angle,  , that
subtends the arc?

44.
Find the area of the following sector. Round to two decimal places.
For #45 – 46 draw the angle.
2
45.
3

45
46.


3
4