Multiple Choice Identify the
choice that best completes the statement or answers the question.


1.

Given , , and , use the Law of Sines to solve the triangle (if possible) for the value of b. If
two solutions exist, find both. Round answer to two decimal places.


2.

Determine a value for b such that a triangle
with and has no solution. Round your
answer to the nearest hundredth.
a.  11.69  b.  2.36  c.  2.95  d.  5.90  e.  31.83 


3.

Determine the area of a triangle having the
following measurements. Round your answer to two decimal places.
a.  23.84 sq. units  b.  28.61 sq. units  c.  21.46 sq.
units  d.  19.07 sq. units  e.  26.22 sq. units 


4.

Given , , and , use the Law of Cosines to solve the triangle for the value of B. Round answer to
two decimal places.


5.

In the figure below, , , and . Use this information to solve the
parallelogram for c. The diagonals of the parallelogram are represented by c and
d. Round answer to two decimal places.
a.  5.52  b.  12.15  c.  10.49  d.  9.25  e.  


6.

In the figure below, , , and . Use this information to solve the
parallelogram for b. The diagonals of the parallelogram are represented by c and
d. Round answer to two decimal places.
a.  12.77  b.  6.03  c.  11.08  d.  9.82  e.  9.40 


7.

Find the component form of vector v with
initial point and terminal point .


8.

Find a unit vector in the direction of .


9.

Find the magnitude and direction angle of . Round direction angle to nearest degree.


10.

Find the component form of v if and the angle it makes with the xaxis is 150°.


11.

Three forces with magnitudes of 95 pounds, 75
pounds, and 146 pounds act on an object at angles 100°, 200°, and 300°, respectively,
with the positive xaxis. Find the magnitude and direction of the resultant force. Round
answers to two decimal places.
a.  41.84 pounds; 256.57°  b.  41.84 pounds; 76.57°  c.  60.18 pounds; 256.57°  d.  60.18 pounds; 76.57°  e.  81.89 pounds; 288.09° 


12.

Given vectors and determine the quantity indicated below.


13.

A force of 45 pounds is exerted along a rope
attached to a crate at an angle of 30° above the horizontal. The crate is moved 23 feet.
How much work has been accomplished? Round answer to one decimal place.
a.  1,035.0 footpounds  b.  896.3 footpounds  c.  1,195.1
footpounds  d.  965.7
footpounds  e.  1,080.4
footpounds 


14.

Find the trigonometric form of the complex number
represented graphically.


15.

Find the trigonometric form of .


16.

Perform the operation shown below and leave the
result in trigonometric form.


17.

Find the product using
trigonometric forms. Leave the result in trigonometric form.


18.

Use DeMoivre's Theorem to find the indicated
power of the complex number. Write the result in standard form.


19.

Use DeMoivre's Theorem to find the indicated
power of the following complex number.
a.   b.  –4,096  c.  2048  d.  4,096  e.  


20.

Find the fourth roots of
Write the roots in trigonometric form.
