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Brooklyn Technical High School
Exam 3 MP3
1)
Pre-calculus Term II
Period_________Date ________Name _________________
Instructor: Mr. Rodriguez
Write the complex number  108  6i in polar form.
Express the argument,  , in degrees where
0    360 .
o
o
Ans
2) Find the product of
3  cos(60o )  i sin(60o ) 
Write the result in simplest standard form
and
1
cos 390o  i sin 390o  .

3
 a  bi  . In your final answer, all expressions should be written as equivalent
expressions with rational denominators.
Ans
3) Divide as indicated and express the result in simplest polar form: Express the argument,  , in degrees
where 0o    360o .
9 cos 35o  i sin 35o

1

cos 0o  i sin 0o 
3

Ans
14
 3

4) Write the complex number 
cos 45o  i sin 45o 
 2



in simplest a  bi form.
Ans
5) Find the 3 cube roots of the complex number 6  6i . Leave the roots in simplest polar form.
Ans


6) For the point given in rectangular coordinates 3 2, 3 2 , find the equivalent polar coordinates  r ,  , where
r  0 and 0o    360o
Ans
7) Sketch the graph of   60o
8) Write the polar equation, solved for r, of the graph at the right.
Ans
9) Write the polar equation, solved for r, of the graph at the right.
Ans
10) Write the polar form of the rectangular equation y  3 x  4 . Write your answer solved for r .
Ans
11) Convert the polar equation r 
1
into rectangular form. Write your answer solved for y explicitly in
3  2 cos 
terms of x.
Ans




12) Find the distance, to the nearest tenth, between the points with polar coordinates 2,30o and 5,125o .
Ans
13) Find the polar coordinates of the intersection points of the curves r  3 and r  6cos ,
where r  0 and 0o    360o
Ans
14) Find the value of r to the nearest tenth, where r  0 , in the equation r 
5  2 tan 
,when   60o .
sec 
Ans
Polar Coordinates
x  r cos
,
y  r sin 
x2  y 2  r 2
tan  
Trigonometric form of complex numbers
a  bi  r (cos   i sin  )
r  a 2  b2
Distance between two points whose coordinates are expressed in polar form
y
x