Precalcus written test.

Ch 10 Test ~ Form S Created Spring 2012 page 1

MATH 2412 ~ PreCalculus Online

Chapter 10 Test ~ Form S

Answer each question carefully and completely showing as much work as possible. For multi-stepped problems you must show your work in order to receive full credit. Using only a calculator to find the answer is not sufficient. In this case, you must use algebra to prove your answer is correct. Unless stated otherwise, the calculator should only be used to check your answer. Make sure that all answers are in simplest form and that you use the correct symbols. If indicated, you must use the requested method in order to receive full credit.

1. Consider the point (-3, �� � ) in the polar plane.

a. Plot the point in the polar plane. Be sure to clearly mark the polar axis and the pole.

b. Convert the polar coordinates to rectangular coordinates.

c. Find two different representations of the point P that have the specified conditions:

• r > 0, ���� � � • r < 0, ��� � ��

Ch 10 Test ~ Form S Created Spring 2012 page 2

2. Convert the rectangular equation � � �� � � to a polar equation. Write your final answer so that r is a function of � .

3. Sketch the graph of the polar equation below by making a table of values. Your table must

contain at least 5 points. (You must make a table of values in order to receive full credit.)

� � ���� 4. Plot the complex number in the complex plane and determine its absolute value. Be sure to

properly mark and label the axes.

� � � � ��

Ch 10 Test ~ Form S Created Spring 2012 page 3

5. Write the complex number in standard polar form. Write the argument in radians using exact values.

� � ��� � ���

6. Find ���� and �� �� if z1 = 10(cos 150° + i sin 150°) and z2 = 8(cos 260° + i sin 260°). Write

your answers in standard polar form with the argument in degrees.

7. Find �� � !" �# � �� "$% � #&'

� and write your answer in rectangular form.

8. Find all complex cube roots of � � �� � (�) Write each root in rectangular form rounding to two decimal places as needed.

Ch 10 Test ~ Form S Created Spring 2012 page 4

9. Represent the vector v in the form ai + bj whose magnitude and direction angle are given

*+* � ��, �� � -��. 10. An airplane was heading due west at 350 mph in still air and encountered a 45 mph tailwind

blowing in the direction S 33° W. Determine the resulting ground speed of the plane and its new bearing.

11. Two tugboats are towing a grain barge out of dangerous shallow water. One tugboat exerts a

force of */�* � (�� pounds in a direction N 41° E. The other tugboat pulls with a force of */�* � -��� pounds in a direction S 18° E. find the magnitude of the resultant force and bearing of the grain barge.

Ch 10 Test ~ Form S Created Spring 2012 page 5

12. Determine the value of a so that the vectors u = -5i – 8j and v = ai + 3j are orthogonal. 13. An object weighing 765 pounds is being hauled up a ramp. The object is held still by a force of

324 pounds. Determine the ramp’s incline angle.