Math 143
Polar Coordinates Problems
1. Change the following from polar coordinates to rectangular coordinates:
(a) (5, )
3
Recall that x = r cos and y = r sin
5
Therefore, x = 5 cos( ) = 5( 1 ) = 2 .
3
2
Similarly, y = 5 sin( ) = 5(
3
3
2)
=
53
2.
Thus,
Math 143, Section 2
Quiz 1
Due: 02/09/2007
Name:
1. (3 points) Determine whether the following functions are even, odd, or neither:
(a) f (x) = x4 + x
Solution:
f (x) = (x)4 + (x) = (1)4 x4 x = x4 x
Since this is not equal to f (x) or to f (x), f (x) is n
Math 143, Section 2
Quiz 3 - Solutions
Name:
1. In the space below, carefully draw the graphs of the following:
1
(a) (3 points) y = 3 tan( 2 t) 2
Notice that this graph have been stretched vertically by a factor of 3, and shifted down 2. Also,
1
the peri
Math 143, Section 1
Quiz 4 - Solutions
03/02/2007
Name:
1. (4 points) Verify the following identity by transforming the left hand side into the right hand side:
1
1
+
= 2 csc2
1 cos 1 + cos
Solution:
1
1 + cos
1 cos
1 + cos + 1 cos
1
+
=
+
=
1 cos 1
Math 143
Quiz 5 - Solutions
Due: 04/02/2007
Name:
This is a Take-Home Quiz. You may use your book and course notes, and you may consult with other
members of the class, but you may not consult with outside tutors (at least not on these specic problems).
1
Math 143, Section 1
Quiz 1 - Solutions
Name:
Due: 1/29/2007
This is a Take-Home Quiz. You may use your book and course notes, and you may work with other members
of the class, but you may not consult with outside tutors (at least not on these specic probl
Math 143
Final Exam Practice Problems
1. Given the angle = 12 radians
(a) Express in terms of degrees, with your answer rounded to the nearest hundredth of a degree.
180
12rad rad 687.55
(b) Draw in standard position
o
687.55
(c) Convert into degree, minu
Math 143, Section 1
Exam 1 - Solutions
01/31/2007
Name:
Instructions: You will have 50 minutes to complete this exam. Calculators are allowed, but this is a
closed book, closed notes exam. I will give credit to each problem proportional to the amount of c
Math 143
Exam 2 - Solutions
02/21/2007
Name:
Instructions: You will have 50 minutes to complete this exam. Calculators are allowed, but this is a
closed book, closed notes exam. I will give credit to each problem proportional to the amount of correct
work
Math 143
Exam 3 - Solutions
03/23/2007
Name:
Instructions: You will have 50 minutes to complete this exam. Calculators are allowed, but this is a
closed book, closed notes exam. I will give credit to each problem proportional to the amount of correct
work