Download Chater 4A Study Guide Answer Section

Chater 4A Study Guide
Short Answer
1. Find the values of the six trigonometric functions
for angle , when
and
.
6. An engineer estimates the angle of elevation to the
top of the building to be 50°. After moving 1.5
meters further away, the angle of elevation was 40°.
How high is the top of the building?
7. Find one angle with positive measure and one angle
with negative measure coterminal with an angle of
104°.
2. A 15-m long ladder rests against a wall at an angle
of
with the ground. How far is the foot of the
ladder from the wall?
Find the exact value of the given trigonometric
function.
8.
3. The upper part of a tree, broken by wind, makes an
angle of 68º with the ground. The horizontal
distance from the root of the tree to the point where
the top of the tree meets the ground is 20 meters.
Find the height of the tree before it was broken.
9.
10.
4. Two boys are on opposite sides of a tower. They
sight the top of the tower at 33º and 24º angles of
elevation respectively. If the height of the tower is
150 m, find the distance between the two boys.
5. A man standing 20 m from a tower estimates the
angles of elevation of the top and bottom of a
flagpole on the tower as 58º and 55º. Calculate the
height of the flagpole.
Find the exact values of the remaining five
trigonometric functions of .
11. Suppose  is an angle in the standard position
whose terminal side is in Quadrant IV and
.
12. Suppose  is an angle in the standard position
whose terminal side is in Quadrant I and
.
18. Determine two coterminal angles (one positive
and one negative) for
.
13. Determine the quadrant in which an angle, ,
lies if
.
19. Rewrite
in radian measure as a multiple of
20. Rewrite
in degree measure.
.
14. Determine the quadrant in which an angle, ,
lies if
radians.
, find the value of  in degrees
15. If
without the aid of a calculator.
21. Find the length of the arc, S, on a circle of
radius 4 feet intercepted by a central angle of
. Round to two decimal places.
16. Using the figure below, if
,
determine the exact value of x.
22. Find the radian measure of the central angle of
the circle of radius 7 feet that intercepts an arc
of length 23 feet.
17. State the quadrant in which  lies if
and
.
23. A car is traveling along Route 66 at a rate of 70
miles per hour, and the diameter of its wheels
are 2.7 feet. Find the number of revolutions per
minute the wheels are turning. Round answer
to one decimal place.
27. The point
is on the terminal side of
an angle in standard position. Determine the
exact value of
.
24. Find the point
on the unit circle that
corresponds to the real number
your results to evaluate
. Use
.
28. Determine the exact value of
.
25. The displacement from equilibrium of an
oscillating weight suspended by a spring is
given by
, where y is the
displacement in centimeters and t is the time in
seconds. Find the displacement when
,
rounding answer to four decimal places.
26. Find the exact value of
shown in the figure below, if
, using the triangle
.
29. If
and
, determine the value of c.
Round to two decimal places.
30. A kite at a height of 70 meters from the ground is
attached to a string inclined at
to the
horizontal. Find the length of the string to the
nearest meter.
Chater 4A Study Guide
Answer Section
SHORT ANSWER
1. sin  =
2.
3.
4.
5.
6.
7.
8.
4
3
5
5
4
3
, cos  = , csc  = , sec = , tan  = , and cot  = .
5
5
4
3
3
4
11.5 m
102.9 m
567.89 m
3.44 m
4.25 m
464°, –256°
2
9.
10.
11.
12.
,
,
,
13. 3rd quadrant
14. 4th quadrant
15.
16.
17. Quadrant II
18.
19.
20.
21.
feet
22.
23. 726.2 rpm
24.
25. –3.9987 cm
26.
27.
,
,
,
,
,
28.
29. 14.15
30. 91 m