Print Name: ____________________
MathB1b / Summer 2011
Exam 4 - Polar Coordinates & Vectors
Read Carefully: Before you start, be sure cell phone is turned off. Anyone caught checking
their cell phone during exam will receive a 0 on it. Once beginning the exam, you must remain
in the room until finished. If you finish early, you may leave the room (check front board to see
what time to return). Relative work must be shown in order to receive credit. Be sure all
answers are simplified and clearly labeled. If space provided is insufficient, additional paper will
be provided. Be sure to clearly label the problems.
Exam consists of two parts (10 sections total between two parts, with each section worth 10
points)
Part I: Calculators are NOT ALLOWED. You may have your scientific calculator on your desk
either face down or with cover on so that it is readily available for Part II. You have up to 35
minutes to finish the first part. You will receive Part II once you turn in part I. Part I can be
turned in early so to have more time on second part. Good luck!
Part I: Non-Calculator Section.
1)
Convert
a. rectangular to polar
4, − 4 3
(
)
b. polar to rectangular
(3, 5π/4)
1
2)
Convert to polar form:
a) x2 + y2 = 16 (Solve for r)
b) 2x + 3y = 5 (Solve for r)
c)
x2 + 2x + y2 – 5y = 3
(Do NOT need to solve for r)
2
3) Convert to rectangular form: (Do NOT need to solve for y)
a) r = 3cosθ + 2sinθ
b) r2cos2θ = 9
c) r = –3cscθ
3
4)
(
Use DeMoivre’s Theorem to find − 2 + i 2
)
20
.
4
5) Find all the cube roots of
3 − i . Leave answers in trigonometric form.
5
Print Name: _____________________
MathB1b / Summer 2011
Exam 3
Part II
Read Carefully: You may use a calculator (No Graphing Calculators), as needed, for this
section. Unless stated, answers should be exact and simplified (this includes rationalizing
denominators). Relative work must be shown in order to receive credit. Partial credit is
rewarded, so it is to your benefit to show steps. Clearly label answers. If additional sheets are
used, write “see scratch paper” next to the appropriate problems and be sure to clearly label the
problems on the additional sheets used. Good luck!
6) Use the vector v drawn below to do the following problems listed below:
a. Draw an equivalent vector that starts at the indicated point above.
b. Write the vector in component form.
c. Calculator Needed. Find the angle (in degrees) and length of the vector. Round
answers to one decimal place.
6
7) Graph the following polar equations:
a) r = 5sin3θ
π/4
b) r = 5sinθ
π/4
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8) Graph the following polar equations.
a) r = 2 – 2cosθ
π/4
b) r = 4 + cosθ
π/4
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9) Given
u = 3,8 , v = 1,−3 ,
find the angle between the two vectors.
9
10) A novice pilot, who did not pass Mr. Klopstein’s Precalculus II class, sets a course of
N 33˚ E at a speed of 215 mph. A 30 mph wind with a direction of N 70˚ E blows him
off course. Perform the following in order to find the resulting speed and direction of the
plane. Round all answers to one decimal places.
a. Find the components of the planes course settings.
b. Find the components of the wind.
c. Use parts a) and b) to find the components of the resulting direction of the plane.
d. What is the resulting speed and direction of the plane.
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