Download Unit TUC The Unit Circle

Precalculus
UNIT TUC
THE UNIT CIRCLE
REVIEW
1)
Convert 220 to radians.
2)
Convert
3)
Convert 3.987R to degrees.
4)
Find one positive and one negative angle coterminal with each of the following angles.
a)
5)
-7p
to degrees.
10
160
b)
-22p
7
c)
9.137
Find the complement and supplement of each of the following angles.
a)
84
MPH/CR 10/11
b)
4p
13
c)
2.631
1
Precalculus
6)
A sector has an arc length of 6 cm and a central angle measuring 60. Find the
radius and the area of the sector.
7)
Find the radius of a sector whose central angle measures
27 p
2
8)
3p
4
and whose area is
ft2.
Find the radius and arc length of a sector whose perimeter is 15 in and whose area
is 14 in2.
MPH/CR 10/11
2
Precalculus
9)
A gear rotates with an angular speed of 420 rpm. Its diameter is 8 inches.
a)
Find the angular speed of the gear in rad/sec.
b)
Find the linear velocity of a point of the circumference of the gear.
c)
How many feet does the gear travel in 2 minutes?
10) P(8, -15) is on the terminal ray of . Evaluate the six trigonometric ratios for .
11) If tan  = -3/7 and 0 <  <
for .
MPH/CR 10/11
3p
2
, evaluate the five remaining trigonometric ratios
3
Precalculus
12) Express each of the following in terms of its reference angle.
a)
sin 110
d)
cot
g)
cot 8.137
17p
4
b)
cos -160
e)
sec
h)
csc -5.312
-9p
11
c)
tan
8p
7
43p
f)
csc
i)
cos 4.153
9
13) Evaluate each of the following giving an exact answer.
a)
sin
d)
cot
MPH/CR 10/11
7p
2
17p
6
4p
b)
cos
e)
sec -5
3
c)
f)
tan
csc
-5p
4
8p
3
4
Precalculus
g)
cot
11p
h)
4
csc -8
i)
cos
-19p
2
14) Evaluate each of the following. Round answers to ten-thousandths.
13p
a)
sin
d)
sec -437
7
-28p
b)
cot
e)
tan 1.678R
11
c)
cos 238
f)
csc -9.650R
15) Evaluate each of the following.
a)
Sin-1
-1
2
b)
Cos-1
d)
æ
3ö
cot ç Sin -1
÷
2 ø
è
e)
csc (Cos-1 -7/25)
MPH/CR 10/11
- 2
2
c)
f)
sec (Tan-1 0)
sin (Tan-1 -15/8)
5