Precalculus Final Exam REVIEW 5
Name:_________________________________Hour: _____
101. GRAPH the following polar coordinates and use the letter to label it on the polar grid.
A
 5, 150° 
B
2,
 45°
  6,
C


D   4, 
2

75° 
E
  3,
 135° 
Convert the following rectangular coordinates to polar coordinates with r  0. Watch your MODE!
102. 0° ≤ < 360° EXACT
1, √3
103. 0    2 nearest 100th for angle
(−3, −4)
104. 0    2 nearest 100th for angle
(7, −24)
105. 0° ≤ < 360° EXACT
(0, −2)
Convert the following polar coordinates to rectangular coordinates. Watch your MODE!
106. 6√2, 225° EXACT
107. 4,
Express in Rectangular ( +
111. 9
38°
108. (10,
) FORM. Watch your MODE!
nearest 100th
115. Express the product: (5
EXACT
112. 4
80°)(7
8 nearest 100th
15°) in Polar FORM.
117. Use DeMoivre's Theorem to find the indicated power of
√2
225°
in Polar FORM.
119. Find the cube ROOTS of 27
0° ≤
60°.
< 360°
Express answers in Polar FORM.
)
EXACT
109. −8,
Express in Polar ( 113. 5 − 5
0° ≤ < 360°
EXACT
110. (7,42°) nearest 100th
)FORM. Watch your MODE!
114. −√3 −
0 ≤ < 2
EXACT
116. Express the product: (3
300°)(8
EXACT
150°) in Polar FORM.
118. Use DeMoivre's Theorem to find the indicated power of
(2 150°) in Polar FORM. 0° ≤ < 360°
120. Find the cube ROOTS of 64
300°.
Express answers in Polar FORM.
VECTORS
121. Find the vector in component form given:
| | = 6, = 300°
EXACT
123. Given:
122. Find the vector in component form given:
| | = 3, = 75° nearest 100th
= −2 − 5
Find the magnitude (exact)
Find the direction (nearest 100th)
125. Given: =< 2, 7 > =< 3, 1
Find:
124. Given:
= 5√3 − 5
Find the magnitude
Find the direction (EXACT)
126. Given: =< −8, −2 > =< 5, −20 >
∙ Find:
127. Find the angle between u and v (nearest 100th of a degree)
Given: =< 2, 7 > =< 3, 1 >
∙ 128. Find the angle between u and v
Given: =< −8, −2 > =< 5, −20 >
Are the given vectors are orthogonal?
129. Find the WORK done by force
object from (2, −8) to (7, 1).
=3 +7
in moving an
130. Find the WORK done by force
object from (1, 1) to (7, −1).
=2 +9
in moving an
131. Katie's plane heads in the direction N 30° W at a speed of
500 mph. Her plane experiences a 24 mph crosswind flowing
due West. Find the true velocity of the plane.
132. Dan's plane heads in the direction of N 30° E at 650 mph.
His plane experiences a 40 mph wind flowing in the direction of
N 60° E. Find the true velocity of the plane.
a.) Find the velocity of the plane in component form <
EXACT
, >.
a.) Find the velocity of the plane in component form <
EXACT
, >.
b.) Find the velocity of the wind in component form <
EXACT
, >.
b.) Find the velocity of the wind in component form <
EXACT
, >.
c.) Find the TRUE VELOCITY of the plane as a vector in terms of i and j.
Nearest 100th
c.) Find the TRUE VELOCITY of the plane as a vector in terms of i and j.
Nearest 100th
d.) Now, find the true speed (magnitude) of the plane in mph. Nearest 100th