MATH INVESTIGATIONS 4 Problem Set: 5 Fall 2013
ID Number____________
Teacher (circle): Condie Dover Krouse Pandya
Prince
Mods: __________
Due Friday, September 27
Note: All answers must be supported with written work/explanation. Show sufficient work and
explanation to justify your answers. Remember you are expected to solve problems marked with NC
without your calculator.
NC
1) Simplify. Show your reasoning.
a) tan   cot   cos 2 
NC
2)
b) csc x  cot x 
sin x
1  cos x
Solve the equation for x in the indicated domain:
2cos 2 ( x)  5sin( x)  1 , 0  x  2
n
1 
Let an   i  , where i  1 , the imaginary unit. You can use your calculator for this
2 
question.
3)
a) State the first 8 terns of an exactly.
n
b) State the first 6 terms of S n where S n   an .
i 1
k
k
k
100
 1  20  1 
1 
c) Compute   i  ,   i  , and   i  accurate to nine decimal places.
k 1  2 
k 1  2 
k 1  2 
d) Without using your calculator, try using the formula for infinite geometric series that we
10
k
1 
developed in the sequence and series unit to compute   i  exactly. [Do you think this
k 1  2 

formula might work for series of complex numbers?]
NC
4) Find the area of a triangle with sides of length 13, 14, and 15.
NC
5) The vertices of ABC are the points A(0,6), B(12,0), and C (0,0). A line through the point
(3,0) bisects the area of the triangle. Find the slope of this line.
PS 5.1
Rev. F13
MATH INVESTIGATIONS 4 Problem Set: 5 Fall 2013
Teacher (circle): Condie Dover Krouse Pandya
Prince
Due Friday, September 27
 1 if n  1,2
6) Consider the sequence: an  
5an  2  2an 1 if n  3
(You may use the sequence mode on your calculator)
a)
b)
State the first 8 terms of the sequence.
a
Let Gn  n 1 . Find G5 .
an
c)
Appproximate lim Gn , accurate to five decmial places.
ID Number____________
Mods: __________
n 
 5 if n  1

7) Consider the sequence: an   3 if n  2
5a  2a
n 1 if n  3
 n2
a)
b)
c)
NC
State the first 8 terms of the sequence.
a
Let Gn  n 1 . Find G5 . State your answer to five decimal places.
an
Appproximate lim Gn , accurate to five decmial places.
n 
8) Evaluate the following infinite continued fraction: 2 
5
.
5
2
5
2
2
5
The
indicates the fraction continues indefinitely in this pattern. State your answer
exactly and as a five decimal-place approximation. Then ponder whether there is a
relationship with problems 6) and 7)?
a1  4
a

9) Consider the sequence: a2  6
. Let Gn  n 1 . State an infinite continued fraction
an
a  3a  7a
n2
n 1
 n
that equals the exact value of lim Gn and use it to calculate this limt.
n 
10) Write the first 10 terms as reduced fractions of the sequence given by:
1, 1+1, 1 
1
1
1
, 1
, 1
,...
1
1
11
1
1
1
11
1
11
PS 5.2
Rev. F13
MATH INVESTIGATIONS 4 Problem Set: 5 Fall 2013
Teacher (circle): Condie Dover Krouse Pandya
Prince
Due Friday, September 27
1a)
1b)
2)
ID Number____________
Mods: __________
3a)
3b)
3c)
3d)
PS 5.3
Rev. F13
MATH INVESTIGATIONS 4 Problem Set: 5 Fall 2013
Teacher (circle): Condie Dover Krouse Pandya
Prince
Due Friday, September 27
4)
5)
6a)
7a)
6b)
7b)
6c)
7c)
PS 5.4
ID Number____________
Mods: __________
Rev. F13
MATH INVESTIGATIONS 4 Problem Set: 5 Fall 2013
Teacher (circle): Condie Dover Krouse Pandya
Prince
Due Friday, September 27
8)
9)
ID Number____________
Mods: __________
10)
PS 5.5
Rev. F13