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Questions for Assignment 1 - Geometry for Architects | MATH 119, Assignments of Mathematics

Illinois Institute of Technology (IIT)Mathematics
Prof. David J. Maslanka

Material Type: Assignment; Professor: Maslanka; Class: Geometry for Architects; Subject: Mathematics; University: Illinois Institute of Technology; Term: Fall 2008;

Typology: Assignments

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Uploaded on 08/16/2009

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Homework Assignments – Math 119-001/002 – Fall 2008
Assignment 1
Due date : Wednesday, September 3, 2008
Section 5.1, Page 155: #1,2,3,5,6.
Section 5.2, Page 160: #1,2,3,5,6,8,10-15,17,21,23.
Section 5.3, Page 163: # 1(a)(c), 2(a)(c)(f), 4,7.
Assignment 2
Due date : Wednesday, September 10, 2008
Section 5.4, Page 167: #3,7,8,12,13,15,16,17,19,24.
Section 5.5, Page 173: #1,3,5,7,9,11,14,16,19,20,25,28.
Additional Exercises
Suppose we generate a regular 7-pointed star as follows:
i) Locate the vertices of the regular 7-gon on a circle and label them consecutively clockwise (or
counterclockwise) about the circle as:
P1 , P2 , P3 , . . . . , P 7 .
ii) Begin at P1 , skip over the next two vertices (P2 and P3) to join it to P4 with a straight
line segment. Then from P4 , skip over the next two successive vertices once again (P5
and P6 in this case), to join it to P7 with a straight segment. Continuing in this way, P7
is joined to P3 , etc.
So we connect: P1 --> P4 --> P7 --> . . . --> P1.
( a ) Find the measure of the interior angle at each vertex of the star formed in the manner
described above.
( b ) What is the total sum of the angles turned by a person who walks around the path
which generates this star?
( c ) Answer parts ( a ) and ( b ) for the case of the 7-pointed star generated by starting at
a vertex, P1 , and skipping over only one successive vertex at each stage. Thus, we
join the vertices in the order: P1 --> P3 --> P5 --> . . . --> P1.
( d ) How many distinct 9-pointed stars are constructible by starting with the vertices of a
regular 9-gon and joining them by “skipping around” in methods similar to those
described above for the 7-gon? Draw them.
Assignment 3
Due date : Wednesday, September 17, 2008
Section 6.1, Page 181: #1(a)(c),2(a)(b),3(a)(h)(p),5,8,9,10,14.
Section 6.2, Page 185: #1,4,7,11,15,20.
Section 6.3, Page 187: #2,5,10,16,17,20,21,22,25,26,33.
Assignment 4
Due date : Wednesday, September 24, 2008
Section 7.1, Page 204: #2,4,9,10,18,22,25,46,49,53,60,67,68,69,73,74,75.
Section 7.2, Page 208: #1,2,3,5,6,7,8,13,14,15,16.
Section 7.3, Page 213: #1(a)(b),7(c)(d),11,12,13.
Section 7.4, Page 221: #12,13,14.
. . . . . . . Exam 1 . . . . . . . . . . . . . . . . . . . Monday, September 29 . . . . . . . . . . . . . . . . . . . . .
Assignment 5
Due date : Wednesday, October 6, 2008
Section 13.1, Page 365: #1,2,5,7,14,15,19,22,23,29,34,36,41,47,53,57,73,78,79.
Section 13.2, Page 368: #1,3,8,11,15,16,17,18,21,22,25,28,33,34.
Section 13.3, Page 372: #4,7,8,15,16,17.
Additional Exercise
Use the distance formula, D, along the surface of the Earth (see page 5 of the text:
http://www.iit.edu/~maslanka/long&lat.pdf ) to find the surface distance between Chicago, IL
(Latitude = 41.8795, Longitude = -87.6243) and each of the cities:
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Partial preview of the text

Download Questions for Assignment 1 - Geometry for Architects | MATH 119 and more Assignments Mathematics in PDF only on Docsity!

Homework Assignments – Math 119-001/002 – Fall 2008

Assignment 1

Due date : Wednesday, September 3, 2008

Section 5.1, Page 155: #1,2,3,5,6.

Section 5.2, Page 160: #1,2,3,5,6,8,10-15,17,21,23.

Section 5.3, Page 163: # 1(a)(c), 2(a)(c)(f), 4,7.

Assignment 2

Due date : Wednesday, September 10, 2008

Section 5.4, Page 167: #3,7,8,12,13,15,16,17,19,24.

Section 5.5, Page 173: #1,3,5,7,9,11,14,16,19,20,25,28.

Additional Exercises

Suppose we generate a regular 7-pointed star as follows: i) Locate the vertices of the regular 7-gon on a circle and label them consecutively clockwise (or counterclockwise) about the circle as: P 1 , P 2 , P 3 ,.... , P 7. ii) Begin at P 1 , skip over the next two vertices ( P 2 and P 3 ) to join it to P 4 with a straight line segment. Then from P 4 , skip over the next two successive vertices once again ( P 5 and P 6 i n this case), to join it to P 7 with a straight segment. Continuing in this way, P 7 is joined to P 3 , etc. So we connect: P 1 --> P 4 --> P 7 -->... --> P 1.

( a ) Find the measure of the interior angle at each vertex of the star formed in the manner described above. ( b ) What is the total sum of the angles turned by a person who walks around the path which generates this star? ( c ) Answer parts ( a ) and ( b ) for the case of the 7-pointed star generated by starting at a vertex, P 1 , and skipping over only one successive vertex at each stage. Thus, we join the vertices in the order: P 1 --> P 3 --> P 5 -->... --> P1. ( d ) How many distinct 9-pointed stars are constructible by starting with the vertices of a regular 9-gon and joining them by “skipping around” in methods similar to those described above for the 7-gon? Draw them.

Assignment 3

Due date : Wednesday, September 17, 2008

Section 6.1, Page 181: #1(a)(c),2(a)(b),3(a)(h)(p),5,8,9,10,14.

Section 6.2, Page 185: #1,4,7,11,15,20.

Section 6.3, Page 187: #2,5,10,16,17,20,21,22,25,26,33.

Assignment 4

Due date : Wednesday, September 24, 2008

Section 7.1, Page 204: #2,4,9,10,18,22,25,46,49,53,60,67,68,69,73,74,75.

Section 7.2, Page 208: #1,2,3,5,6,7,8,13,14,15,16.

Section 7.3, Page 213: #1(a)(b),7(c)(d),11,12,13.

Section 7.4, Page 221: #12,13,14.

....... Exam 1................... Monday, September 29.....................

Assignment 5

Due date : Wednesday, October 6, 2008

Section 13.1, Page 365: #1,2,5,7,14,15,19,22,23,29,34,36,41,47,53,57,73,78,79.

Section 13.2, Page 368: #1,3,8,11,15,16,17,18,21,22,25,28,33,34.

Section 13.3, Page 372: #4,7,8,15,16,17.

Additional Exercise

Use the distance formula, D , along the surface of the Earth (see page 5 of the text: http://www.iit.edu/~maslanka/long&lat.pdf ) to find the surface distance between Chicago, IL (Latitude = 41.8795, Longitude = -87.6243) and each of the cities:

i) Cairo, Egypt: Latitude = 30.0571, Longitude = 31. ii) Bogotá, Columbia: Latitude = 4.6473, Longitude = -74. iii) Cape Town, South Africa: Latitude = -33.9160, Longitude = 18. iv) Beijing, China: Latitude = 39.9082, Longitude = 116. v) Sydney, Australia: Latitude = -33.8671, Longitude = 151.

Assignment 6

Due date : Monday, October 20, 2008

Section 14.1, Page 382 #31.

Section 14.4, Page 399 #23,24.

Additional Exercises #1 – 8 (below).

Assignment 7

Due date : Friday, October 31, 2008

Section 15.1, Page 419 #1,2,3,5,10,12,17,21,27,33,43.

Section 15.2, Page 425 #1,2,3,5,9,10,11,12,13,14,15.

Section 15.3, Page 431 #1,2.

Additional Exercises #1 – 12 (below).

Instructions In problems 1- 4 plot at least once cycle of each of the sine or cosine waves. Plot all of the curves for each problem on a single graph. Do not use a calculator but rather follow the method outlined in the text, section 14-2, on pages 383-386.

In each problem, you should obtain the graph of equations (b) and (c) from that of equation (a) by using a suitable horizontal or vertical shift in each instance. Be certain to: ( i ) Locate the coordinates of all the zeros ( i.e. the points of the form ( x , 0 ) ) on your plots. ( ii ) Locate the coordinates of all the extreme points (i.e. the points of the form ( x , a ) and ( x , – a ) where a = amplitude of the graph). (iii) Locate the coordinates of all points of the form: ( x , a / 2 ) and ( x , – a / 2 ) where a = amplitude of the graph.

1. ( a ) y = 2 sin( 3 x ) ( b ) y = 2 sin ( 3 x – π ) ( c ) y = 2 sin ( 3 x – π ) – 4

2. ( a ) y = cos ( x ) ( b ) y = cos ( x + π / 3 ) ( c ) y = cos ( x + π / 3 ) + 1

3. ( a ) y = –4 sin( 2 x ) ( b ) y = – 4 sin( 2 x – π / 4 )

4. ( a ) y = –cos ( x / 2 ) ( b ) y = – cos ( x / 2 + π )

In problems 5 – 8, plot at least two cycles of each periodic function. Plot both of the curves for each problem on a single graph. Use shifting (if relevant) to obtain the graph of equation ( b ) from that of equation ( a ).Be certain to: ( i ) Locate the coordinates of all the zeros on your plots. ( ii ) Locate all the vertical asymptotes for your plots.

5. ( a ) y = tan ( 4 x ) ( b ) y = tan ( 4 x – π / 2 )

6. ( a ) y = 2 sin( 3 x ) ( b ) y = 2 csc ( 3 x ) 7. ( a ) y == –cos ( x / 2 ) ( b ) y = = –sec ( x / 2 )

8. ( a ) y = cot ( 3 x ) ( b ) y = cot ( 3 x ) + π / 2

For each equation, 1 – 12, do the following:

(a) Graph the equation in the rectangular r θ - plane over the specified θ range.

(b) Graph the equation in polar coordinates in the xy -plane where x = r cos θ and y = r sin θ (c) Convert the equation for the polar graph from (b) to Cartesian coordinates.

  1. r = 6 , 0 < θ < 2π 2. θ = 3

π , 3

π < θ < 3

π

  1. r = 8 + 6 cos θ, 0 < θ <2π

  2. r = 7 + 7 cos θ, 0 < θ < 2π 5. r = 5 + 9 cos θ, 0 < θ < 2π 6. r = 3 + 11 cos θ, 0 < θ < 2π

  3. r = 2 sin 2θ, 0 < θ < 2π 8. r = 3 sin 3θ, 0 < θ < π 9. r = 3 sin θ, 0 < θ < π

  4. r = sinθ

3 , 0 < θ < π 11. r^2 = 9 sin 2θ, 0 < θ < 2

π

  1. r 2 = 16 cos 2θ, - 4

π < θ < 4

π

Assignment 10

Due date : Monday, December 1, 2008

Section 20.4, Page 584 #1,2,5,6,7,14,15,31,33,35.

Additional Exercises #1 – 5 (below).

1. Find the equation of the parabola with vertex: V = ( 0 , 0 ) and passing thru the points: ( 2 , 3 ) and ( –2 , 3 ). 2. Find the equation of the parabola with focus F = ( 1 , 1 ) and the directrix D: x + y = 0 in two ways:

( a ) By using the fact that : Q = ( x , y ) on P ⇔ d( Q , F ) = d ( Q , D ).

( b ) By rotating the parabola y 2 =2 2 x by 45 o^ about its axis and translating

its graph + 2

1 units horizontally and + 2

1 units vertically.

3. Find the equation of the tangent line to x 2 = –5 y at ( 5 , –5 ) by using only the techniques of analytic geometry. 4. Find the equation of the tangent line to y 2 = –16 x that is parallel to the line x + y = 1. 5. The towers of a suspension bridge are 500 feet apart and extend 100 feet above the road surface. The main cables between the towers reach within 10 feet of the road at the center of the bridge, and there are vertical supporting cables every 10 feet. Find the lengths of those supporting cables at 100 foot intervals.