(These problems are for Chapter 8, starting with 8th edition)
Section 7.1 Section 7.2 Section 7.3 Section_7.4 Section 7.5
(8.1 - 8.5 starting with 8th edition)
Section 7.1 (8.1 starting with 8th edition)
Find the reference angle of each angle.
A-12. 60 degSection 7.1 (8.1 starting with 8th edition)
Find the reference angle of each angle.
A-12. 30 deg
A-18. 5`pi/3
A-20. 11`pi/4
A-24. -11`pi/6
Find exact values:
A-30. sin 240 deg
A-36. cos (-2`pi/3)
A-40. cot (-120 deg)
A-42. cot (`pi/2)
A-48. tan 78 deg - cot 12 deg
A-50. cos 50 deg/sin 40 deg
A-54. cot 40 deg - sin 50 deg/sin 40 deg
A-60. If sec `theta = 4, find the exact value of :
* a) sec (-`theta)
* b) cot `theta
* c) csc (90 deg-`theta)
* d) sin `theta
A-66. find the exact value of sin 1 deg +sin 2 deg+ sin 3 deg+ . . . . sin 358
deg+ sin 359 deg.
A-72. (See figure, Problem 7.1 #72 in Sullivan's 6th edition. If using a
different edition email instructor with number of edition). A ladder of length L
is being carried around a corner from a hall 3 ft wide to a hall 4 ft wide. The
ladder makes angle `theta with the wall of the 3-foot-wide hall, and it just
touches the outside wall of each hall. Find the length L of the ladder in terms
of `theta.
A-78. Sketch an isosceles triangle and label the equal sides both a, indicating
length a along each of the equal sides, and the two equal angles `theta at the
base of each side. Show that the area of the triangle is A = a^2 sin(`theta)
cos(`theta).
Use a right triangle with side a opposite angle `alpha, side b opposite angle
`beta and side c opposite a right triangle. Then, using the given information,
solve the triangle.
B-6. b=8,`alpha=25 `deg;find a,c, and `beta
B-10. c=10,`alpha=40 `deg; find b, a, and `beta
B-12. a=5,b=15;find c, `alpha and `beta
B-18. A right triangle contain an angle of `pi /16 radian. If one leg is of
length 2 meters, what is the length of the hypotenuse?
B-20. The hypotenuse of a right triangle is 3 feet. If one leg is 1 foot, find
the degree measure of each angle.
B-24. Finding the Distance of a ship from shore A ship offshore from a vertical
cliff known to be 100 feet in height, takes a sighting of the top of the cliff.
If the angle of elevation is found to be 25 `deg, how far offshore is the ship?
B-36. Finding the height of a tower A guy wire 80 feet long is attached to the
top of a radio transmission tower, making an angle of 25 `degwith the ground.
How high is the tower?
B-40. Security, a security camera in a neighborhood bank is mounted on a wall 9
feet above the floor. What angle of depression should be used if the camera is
to be directed to a spot 6feet above the floor and 12 feet from the wall?
B-42. Finding the bearing of a ship a ship leaves the port of Miami with a
bearing of S80 `deg E and a speed of 15 knots. After 1 hour, the ship turns 90 `degtoward
the south. After 2 hours, maintaining the same speed, what is the bearing to the
ship from the port?
B-48. Determining the height of an aircraft Two sensors are spaced 700 feet
apart along approach to a small airport. When an aircraft is 2 miles from the
airport, the angle of elevation from the first sensor to the aircraft is 20
`deg, and from the second sensor to the aircraft if 15 `deg. How high is the
aircraft at this time?
B-50. Construction a ramp for wheel chair accessibility is to be constructed
with an angle of elevation of 15 `deg and final height of 5 feet. How long is
the ramp?
Section 7.2 (8.2 starting with 8th edition)
Find the information to solve each of the following triangles.
10. c = 5, `alpha = 45 `deg, `beta = 40 `deg
12. alpha = 70 deg; `beta = 60 deg, c = 4
18. `alpha = 50 `deg, `gamma = 20 deg, a = 12
20. `alpha = 70 deg, `beta = 60 `deg, c = 14
24. a = 2, c = 1, `alpha = 120 deg
28. b = 4, c = 5, `beta = 40 deg
30. b = 2, c = 3, `gamma = 100 deg
36. b = 4, c = 5, `beta = 40 deg
40. The navigator of a ship at sea spots two lighthouses that she knows to be 3
miles apart along a straight seashore. She determines that the lighthouse are at
15 deg and 35 deg angles from the direct line of sight from the ship to the
shoreline.
a) How far away is the ship from the first lighthouse?
b) How far away is the ship from the second lighthouse?
c) How far is the ship away from the shore?
54. The distance from the Sun to Earth is approximately 149,600,000 km and the
distance from the Sun to Venus is approximately 57,910,000 km. The elongation
angle is the angle formed between the line of sight from Earth to the Sun and
from the Earth to Venus. Suppose that this angle is 10 `deg. What are the
possible distances between the Earth and Venus?
Section 7.3 (8.3 starting with 8th edition)
Solve each triangle with the given information.
10. b = 3, c = 4, `alpha = 30 deg
14. b = 4, c = 1, alpha = 120 deg
20. a = 6, b = 4, `gamma = 60 deg
26. a = 4, b = 5, c = 3
30. a = 4, b = 3, c = 6
32. The height of a radio tower is radio tower is 500 feet,and the ground on one
side of the tower slopes upward at an angle of 15 deg. How long should a guy
wire be if it is to connect to the top of a tower and be secured at a point on
the sloped side 100 feet from the base of the tower? How long should a second
wire be on the flat side to connect to the middle of the tower and be secured
100 feet away?
36. An airplace flies from Fort Myers to Sarasota, a distance of 150 miles, and
the turns through an angle of 50 deg and flies to Orlando, a distance of 100
miles. How far is it from Ft. Myers to Orlando and through what angle should the
pilot turn at Orlando to return to Ft. Myers?
42. On a Little League baseball field, the distance from home plate to the fence
in dead center is 280 feet. How far is it from the fence in dead center to third
base considering the length between bases on this field is 60 feet.
Section 7.4 (8.4 starting with 8th edition)
Find the area of the given triangles. Round answers to the nearest two decimal
places.
10. a = 2 , c = 1, `beta = 10 deg
14. b = 4, c = 1, `alpha = 120 deg
18. a = 6, b = 4, `gamma = 60 deg
24. a = 4, b = 3, c = 6
28. A cone is formed from a base circle with 24 ft diameter, a 100 deg sector is
removed from the base. Find the area of the cone obtained when you fold join the
cut edges.
Section 7.5 (8.5 starting with 8th edition)
6. An object attached to a coiled spring is pulled down a distance of 10 cm then
released. It completes one cycle of simple harmonic motion every three seconds.
Write an equation for its motion assuming that at t = 0 the object is at its
resting position and moving downward.
In problems 10 and 12, answer the following:
a. Describe the motion of the object
b. What is the maximum displacement for its resting position?
c. What is the time required for the oscillation?
d. What is the frequency?
10. d=3 sin t
12. d=5 cos(`pi /2)t
Graph each damped vibration curve for 0 <= x <= 2 `pi
18.y=e^( -x / (2`pi)) * cos x
20.y=e^( -2x / `pi) * sin x
24.Graph
* y= 1/x cos x,
* y= 1/(x^2) cos x and
* y= 1/(x^3) cos x
for x>0. What pattern do you observe?