~1~
degree
degree
~2~
~3~
~4~
~5~
Matching: Identify each of the following graphs.
a)
c)
b)
f)
d)
e)
h)
i)
g)
1)
y  sin( x)
2)
y  cos( x)
3)
y  tan( x)
4)
y  sec( x)
5)
y  cot( x)
6)
y  sin 1 ( x)
7)
y  Arccos( x)
8)
y  csc( x)
9)
y  tan 1 ( x)
~6~
1. Using the graph of sine, what is the restricted the domain, in radians, so that its inverse will be a function? Draw
a sketch.
2. Using the graph of cosine, what is the restricted domain, in radians, so that its inverse will be a function? Draw a
sketch.
3. Using the graph of tangent, what is the restricted domain, in radians, so that its inverse will be a function? Draw
a sketch.
4. The function
is defined in such a way that
1)
3)
2)
4)
5. The function y  sin( x) is defined in such a way that
is a function. What can be the domain of
is a function. What can be the domain of
1)
0  x   
3)


  x  
2

2)
0  x  2 
4)

 
  x  
2
 2
6. The function y  cos( x) is defined in such a way that
is a function. What can be the domain of
1)
0  x   
3)


  x  
2

2)
0  x  2 
4)

 
  x  
2
 2
~7~
?
?
?
Directions: Round sides to the nearest tenth of a unit. Round angles to the nearest degree.
1) In triangle ABC, a=12, b=15, and mC  60 . Find c.
2) If mC  82 , mA  55 , and a=8, find c.
3) In triangle ABC, a=20, b=16, and c=32. Find mB .
4) In triangle ABC, if mB  110 , mA  30 , and a=15, find b.
~8~
5) In triangle ABC, a=20, c=25, and mB  98 . Find b.
6) In triangle ABC, if mA  16 , b=92, and mB  120 find c.
7) In triangle ABC, b=20, c=23, and a=30, find mA .
8) If mA  75 , mB  55 , and c=5, and find a.
9) In triangle ABC, a=19, b=14, and c=12. Find mC .
~9~
1) A ship at sea heads directly toward a cliff on the shoreline. The accompanying diagram
shows the top of the cliff, D, sighted from two locations, A and B, separated by distance S.
If mDAC  27 , mDBC  50 , and S = 25 feet, what is the height of the cliff, to the
nearest foot?
2) A cross-country trail is laid out in the shape of a triangle. The lengths of the three paths
that make up the trail are 2000 m, 1200 m, and 1800 m. Find to the nearest degree the
measure of the smallest angle formed by the legs of the trail.
3) If the base angle of an isosceles triangle measures 34 and the base of the triangle is 8
inches, find the length of other sides of the triangle to the nearest tenth.
4) In a triangle, two sides that measure 4 cm and 7cm form an angle of 60°. Find the measure
of the smallest angle of the triangle to the nearest degree.
~ 10 ~
1
5) In ABC , AC  18, BC  10, and cos C  . find the area of ABC to the nearest tenth of a
2
square unit. (Hint: Find angle C first).
6) In an isosceles triangle, the vertex angle is 30º and the base
measures 12 cm. Find the perimeter of the triangle to the nearest
integer.
7) A triangular field has side lengths of 100 feet, 250 feet, and 300 feet. Find the area of the
field to the nearest square foot.
8) In the accompanying diagram, angle R is an obtuse angle, not a right angle.
Find the length of PQ to the nearest foot.
~ 11 ~
Solve the following problems.
1) If forces of 47 pounds and 52 pounds act on object such that the angle between them is
70, what is the resultant force to the nearest pound?
2) Two forces of 42 newtons and 57 newtons act on an object with a resultant of 70
newtons.
a.
Find to the nearest degree, the angle between two applied forces.
b.
Next, find the angle between the resultant and the larger force to the
nearest degree.
3) Two forces act on a body so that the resultant has a force of 135 newtons. If the angles
between the resultant and each of the forces are 72 degrees and 12 degrees, find the
magnitude of the larger applied force to the nearest tenth of a newton.
~ 12 ~
4) Two forces act on an object. The first force has a magnitude of 75 pounds and makes an
angle of 34 degrees with the resultant. The magnitude of the resultant is 110 pounds.
c. Find the magnitude of the second applied force to the nearest tenth of a pound.
d. To the nearest tenth of a degree, find the angle the second force makes with the
resultant.
5) Two forces of 80 pounds and 100 pounds act on object such that the angle between them
is 105.
e. What is the resultant force to the nearest pound?
f. What is the angle between the resultant force and the smaller force to the
nearest minute?
~ 13 ~