CS1112 Section Exercise 3
1 Which quadrant? (re-visited)
[Last week’s challenge question] Write a script using nested conditional statements without elseif to determine
in which quadrant a user-input value of Adegrees belongs. Assume that the user may enter any non-negative
number. For example, 725◦is the same, and should be treated, as 5◦. (Hint: the function rem that you saw last
week might be useful.) To avoid ambiguity, we use the following convention:
Quadrant is
1if0≤A<90
2 if 90 ≤A<180
3 if 180 ≤A<270
4 if 270 ≤A<360
2 Multiples of k
The following program reads an integer kand outputs all the multiples of kup to 1000. Fill in the blank.
k = input(’Please enter a positive integer smaller than 1000: ’);
for j = ______________________
fprintf(’%d ’, j);
end
fprintf(’\n’);
3 Approximate π
[Modified from Insight Exercise P2.1.5] For large n,
Tn=1+ 1
22+···+1
n2=
n
X
k=1
1
k2≈π2
6
Rn=1−1
3+···− (−1)n+1
2n−1=
n
X
k=1
(−1)k+1
2k−1≈π
4
giving two different ways to estimate π:
τn=p6Tn
ρn=4Rn
Write a script that displays the value of |π−ρn|and |π−τn|for n= 100 : 100 : 1000 in one table.
4 Divisors
Write a script to print all the numbers between 1 and n, exclusive, that divide n(without a remainder using
integer division). nis a user input positive integer. (Hint: Remember function rem?)
Optional Challenge Question
Refer to Question 4 and write a script to print the prime numbers that divide n. Do not use any built-in functions
other than rem.
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