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加拿大数学assignment格式,加拿大Math Assignment写作格式辅导
Luran(Lori) Zhou
2012/2/24
Year 11 Mathematic B
Teacher: Miss Roach
This assignment is about a cyclone is bearing down on the coast of China due east of Hong Kong and due south of Shang Hai, moving directly towards the town Yi Chang. The angles and the distances about the cyclone and towns were calculated by using Trigonometric functions and application.
Q1.Choose a town between Hong Kong and Shang Hai anduse the Internet site to find the latitude and the longitude of all the towns.
City The latitude the longitudeShang Hai 31° 13' 48" N 121° 28' 12" E
Hong Kong 22° 17' 2" N 114° 9" E
Yi Chang 30 °42' N 111° 16' 48" E
cyclone 22° 17' 2" N 121° 28' 12" E
Yi Chang was chosen as the town.
The web was used to find the longitude and the latitude of all the towns and cities.
The latitude and the longitude of Hong Kong: 22° 17' 2" N, 114° 9" E
The latitude and the longitude of Shang Hai: 31° 13' 48" N, 121° 28' 12"E
The latitude and the longitude of Yi Chang: 30 °42' N, 111°16' 48" E
The latitude and the longitude of the cyclone: 22° 17' 2" N,121° 28' 12" E
Q2. Use the Internet to find and record the distance and initial bearing between the towns and cyclone.
From To Distance Initial bearingHong Kong Shang Hai 1231km 034°33′47″
Shang Hai cyclone 994.8km 180°00′00″
Hong Kong cyclone 753.1km 088°36′38″
Yi Chang Hong Kong 978.3km 162°22′04″
Yi Chang cyclone 1379km 130°19′00″
The website was used to find all the data above.
Q3. Using measurements and sine and cosine rule to find all angles from the above diagram.
The cosine rule formula was used to calculate∠A:cosA=(b^2 〖+c〗^2-a^2)/2bc
cos∠A=(〖978.3〗^2 〖+1379.0〗^2-〖753.1〗^2)/(2×978.3×1379.0)
∠A=〖cos〗^(-1) ((〖978.3〗^2 〖+1379.0〗^2-〖753.1〗^2)/(2×978.3×1379.0))
∠A=31°51'50″
The sine rule formula was used to calculate ∠ADBand∠ABD:
a/(sin A)=b/sinB=c/sinC
BD/(sin A)=AB/(sin∠ADB)
753.1/(sin31°51'50″)=978.3/(sin∠ADB)
∠ADB=sin^(-1) （(978.3×sin?〖31°〖51〗^' 〖50〗^″ 〗)/753.1）
∠ADB=43°〖17〗^' 44″
BD/(sin A)=AD/(sin∠ABD)
753.1/(sin31°51'50″)=1379.0/(sin∠ABD)
∠ABD=sin^(-1) （(1379.0×sin?〖31°〖51〗^' 〖50〗^″ 〗)/753.1）
∠ABD=75°9^' 34″
According to diagram, ∠ABD is obtuse
So ∠ABD=180°-75°9^' 34″=104°〖50〗^' 26″
Verify the angles:
∠ABD+∠ADB+∠A=104°〖50〗^' 26″+43°〖17〗^' 44″+31°51'50″=179°〖59〗^' 〖36〗^″≈180°
In △ABD, the three angles can be added into 180°.
The cosine rule formula was used to calculate∠A:
cosA=(b^2 〖+c〗^2-a^2)/2bc
cos∠C=(〖CD〗^2 〖+CB〗^2-〖BD〗^2)/(2×CD×CB)
cos∠C=(〖994.8〗^2 〖+1231〗^2-〖753.1〗^2)/(2×994.8×1231)
∠C=〖cos〗^(-1) ((〖994.8〗^2 〖+1231〗^2-〖753.1〗^2)/(2×994.8×1231))
∠C=37°42'4″
The sine rule formula was used to calculate ∠CBDand∠CDB:
a/(sin A)=b/sinB=c/sinC
BD/(sin C)=CD/(sin∠CBD)
753.1/(sin37°42'4″)=994.8/(sin∠CBD)
∠CBD=sin^(-1) （(994.8×sin?〖37°〖42〗^' 4^″ 〗)/753.1）
∠CBD=53°〖52〗^' 57″
BD/(sin C)=CB/(sin∠CDB)
753.1/(sin37°42'
4″)=1231/(sin∠CDB)
∠CDB=sin^(-1) （(1231×sin?〖37°〖42〗^' 4^″ 〗)/753.1）
∠CDB=88°〖24〗^' 22″
Verify the angles:
∠CDB+∠CBD+∠C=88°〖24〗^' 〖22〗^″+53°〖52〗^' 〖57〗^″+37°〖42〗^' 4^″=179°〖59〗^' 〖23〗^″≈180°
In△CBD，the three angles can be added to 180°.?
Q4. Find the area formed by the lines joining these towns from the above diagram.
The surface areaformula was used:SA = 1/2 bc×sinA
SA ?ABD=1/2×AB×AD×sin∠BAD
=1/2×978.3×1379.0×sin31°51'50″
=356090.17〖km〗^2
SA ?CBD=1/2×CB×CD×sin∠BCD
=1/2×994.8×1231×sin37°42'4″
=374447.03〖km〗^2
The area of triangle ABD is 356090.17km2，the area of triangle CBD is 374447.03Km2.
Q5. Verify the bearing using trigonometry and the latitude and longitude values from the diagram below.
∠FAD=∠ADB=43°〖17〗^' 〖44〗^″∠EAB=∠EAF+∠FAD+∠BAD=90°+43°〖17〗^' 〖44〗^″+31°〖51〗^' 〖50〗^″
=165°9'34″
The initial bearing of Yi Chang to Shang Hai calculated by using latitude and longitude is 162°22′04″, and the trigonometry calculation is 165°9'34″
Q6. Write any assumptions, strengths and/or limitations relating to the calculations above.
Assumptions:It wasassumed to happenin 2 dimension not 3 dimensions. The earth should be a sphere, but it consider as a flat surface. The distance between the towns and the cyclone is a straight line not curved line.
It’s was assumed that the centre of the towns, cities and cyclone are joined together.
The calculations which were provided by the websites were assumed to be accurate.
Limitations:
The calculations of the questions were not very accurate, they were approximate value.For example, most of the angles were approximate to the neatest seconds.
The distance between each town and cityfrom the websites may not be accurate.
Q7. Find the distance from the weather to each town when the angle to the other town has reduced by a half.
In the diagram above, the cyclone was assumed to move directly to the town Yi Chang on AD. And when the cyclone moved to D’, the angle BCD was divided in half by CD’. The cyclone D’ and each town are joined together, A, E, D’, D are on the same line.According to Q2,
∠A=31°〖51〗^' 〖50〗^″,∠ADB=43°〖17〗^' 〖44〗^″,∠ABD=104°〖50〗^' 26″,
∠C=37°42'4″, ∠CBD=53°〖52〗^' 〖57〗^″, ∠CDB=88°〖24〗^' 22″
∵CD’ divided ∠BDC in half
∴∠BCD^'=∠DCD^'=1/2×∠BDC=1/2×37°〖42〗^' 4^″=18°51'2″
∠CDD^'=∠CDB-∠ADB=88°〖24〗^' 〖22〗^″-43°〖17〗^' 〖44〗^″=45°6'38″
In △CDD’, ∠DCD'=18°〖51〗^' 2^″, ∠CDD'=45°6^' 〖38〗^″, CD=994.8km
∠CD^' D=180°-∠DCD^'-∠CDD^'=180°-18°〖51〗^' 2^″-45°6^' 〖38〗^″=116°2'20″
The sine rule formula was used:
a/(sin A)=b/sinB=c/sinC
CD'/(sin ∠CDD')=CD/(sin∠CD'D)
CD'/(sin45°6^' 〖38〗^″ )=753.1/(sin116°2'20″)
CD'=(753.1×sin45°6^' 〖38〗^″)/(sin116°2'20″)
CD^'=784.41km
DD'/(sin ∠DCD')=CD/(sin∠CD'D)
DD'/(sin18°51'2″)=753.1/(sin116°2'20″)
DD'=(753.1×sin18°51'2″)/(sin116°2'20″)
DD^'=270.81km
〖AD^'=AD-DD〗^'=1379-270.81=1108.19km
In △CBD’, ∠DCD'=18°〖51〗^' 2^″, CD’=784.41Km, CB=1231km
The cosine rule formula was used
a^2=b^2+c^2-2bccosA
〖BD^'〗^2=〖CB〗^2+〖CD^'〗^2-2×CB×CD^'×cos∠BCD'
〖BD^'〗^2=〖1231〗^2+〖784.41〗^2-2×1231×784.41×cos18°〖51〗^' 2^″=303024.3686
BD^'=550.48km
The distance from the weather to Hong Kong is550.48km;from the weather to Yi Chang is 1108.19km and from the weather to Shang Hai is 784.41km.
Q8. Write any assumptions or approximations that are relevant to the calculations.
Assumptions:
The cyclone was assumed to move straight on a line to the town.
The centre of the town, cities and cyclone were joined together.
It happened in a flat surface not on a sphere.
The data form the websites were accurate enough.
Approximations:
All the angles were approximate to the nearest seconds, and all the distances were approximate to 2 decimal place.
The calculations from the websites were approximate numbers.
看完了上述关于加拿大Math Assignment写作格式的相关辅导后，各位是否也都清楚了国外大学数学作业写作的格式呢？当然除了各式上的困扰外，也有不少的留学生们在读懂Math作业的题意后，却无从下手不知道该如何去解题，此时需要加拿大Math辅导的你就可以联系我们哦。
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