chapter 4 test 2012 sections 1-4
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Pre-Calculus
Chapter 4: Trigonometric Functions
NAME:
DATE:
Chapter 4 TEST
NON-CALCULATOR
Please read all of the directions carefully and
show all of your work to receive full credit. Good luck!
1.
Evaluate the six trigonometric functions of
. Leave your answers as completely simplified expressions.
(6 points)
sin
_____
csc
_____
cos
_____
sec
_____
tan
_____
cot
_____
2.
Rewrite each degree measure in radians and each radian measure in degrees.
(2 points each)
a.
94
b.
355
c.
12
d.
3
10
3.
Find the value of
x
and
y
.
Completely simplify your answers.
(4 points each)
a.
b.
x =
x =
y =
y =
4.
Find the arc length of a sector with a radius of 12 feet and a central angle of 48
. (3 points)
12
10
θ
5.
Find the complement and supplement of the angle. (4 points)
5
6
Complement:
Supplement:
6.
In which quadrant(s) must
lie for cos
< 0? (2 points)
7.
Evaluate the 6 trigonometric functions of
2
. (3 points)
sin
_____
2
csc
_____
2
cos
_____
2
sec
_____
2
tan
_____
2
cot
_____
2
8.
Given
3
cos
7
, find the exact values for other five trigonometric functions of
.
Leave your answers as
completely simplified expressions. (6 points)
sin
_____
csc
_____
sec
_____
tan
_____
cot
_____
9.
Find the point (
x , y
) on the unit circle that corresponds to the real number
t
.
(2 points each)
a.
5
6
t
b.
4
3
t
c.
7
4
t
10. If the coordinate
3,
9
lies on the terminal side of
, evaluate the 6 trigonometric functions of
.
Leave your answers as completely simplified expressions. (8 points)
sin
_____
csc
_____
cos
_____
sec
_____
tan
_____
cot
_____
11. Name the reference angle for
7
5
.
Sketch both
and ’.
(4 points)
θ
θ
12. Evaluate each function: (4 points each)
a.
120
tan
b.
23
sec
6
c.
4
7
sin
d.
cot 510
Pre-Calculus
Chapter 4: Trigonometric Functions
NAME:
DATE:
Chapter 4 TEST
CALCULATOR
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Please read all of the directions carefully and
show all of your work to receive full credit. Good luck!
13. Solve the right triangle. Leave your answers rounded to the nearest tenth, where necessary.
(4 points)
14. Hurricane Sandy has left a tree broken in my backyard. The top of the tree branches are touching the
ground 13 m from the trunk of the tree. The top of the tree also makes a
29
with the ground. How tall
was the tree before it was broken? Round your answer to the nearest tenth. (4 points)
15. There is a little girl trapped on the 4
th
floor of a building that has caught fire. The 4
th
floor is 54 feet off the
ground and a fire truck is 25 feet from the building. At what angle does the ladder need to be placed in
order for the firefighters to reach the little girl?
Round your answer to the nearest tenth. (4 points)
16. An airplane leaves the runway climbing at
18
with a speed of 275 feet per second. Find the altitude of
the plane after 1 minute.
Round your answer to the nearest tenth. (4 points)
17. The circular blade on a saw rotates at 2400 revolutions per minute and has a diameter of 4 inches.
a.
Find the angular velocity of the blade in radians per second. (2 points)
b.
Find the linear velocity of the blade tip in inches per second. Round your answer to the nearest
tenth. (3 points)
18. A tire of radius 20 inches rotates 65 times every minute.
What is the linear speed in miles per hour to the
nearest tenth?
(5 points)