8/10/2019 maths assignment.doc

http://slidepdf.com/reader/full/maths-assignmentdoc 1/6

  Year 11 Mathematics B  Tides and Period Functions

  Assessment 2.2  Name: Troy Rong

Introduction

Sine and cosine are two o the !eriod unctions. The !rimiti"e !eriod o the sine or cosine is

a u## circ#e$ i.e. 2% radians or &'( degrees.

 

Tides are the rises and a##s o sea #e"e# caused )y the com)ined eect o rotation o the

*arth and the gra"itation o the Moon and the Sun. The tides occur with a !eriod o 

a!!ro+imate#y 12 and a ha# hours and are in#uenced )y the sha!e o the near,shore )ottom. .

Period unctions can )e used or !redicting the tide in a ew days.

KAPS 1 :The charts )e#ow are the source data rom the we)site and recorded in a a!!ro!riate ta)#e.

A## times ha"e )een con"erted to decima#s in hours.

 

Tue 22 Wed 23 Thu 24 Fri 25 Sat 26 Sun 27 Mon 28  

Time Ht Time Ht Time Ht Time Ht Time Ht Time Ht Time Ht

0350 0.04  0421 0.13  0454 0.22  0534 0.31 0103 0.78 0234 0.77 0357 0.82

1031 1.46 1115 1.41 1203 1.34 1300 1.26 0631 0.39 0755 0.43  0924 0.42 

1644 0.20  1737 0.31 1838 0.40  1952 0.45  1406 1.22 1518 1.21 1622 1.24

2230 1.10 2310 0.96 2357 0.85 2111 0.44  2216 0.39 2306 0.32 

8/10/2019 maths assignment.doc

http://slidepdf.com/reader/full/maths-assignmentdoc 2/6

  Year 11 Mathematics B  Tides and Period Functions

  Assessment 2.2  Name: Troy Rong

Time Ht

Tue 22    3.8 0.04 

10.5 1.46

16.7 0.2 

22.5 1.1

Wed 23    28.4 0.13 

35.3 1.41

41.6 0.31

47.2 0.96

Thu 24    52.9 0.22 

60.1 1.34

66.6 0.4 

72 0.85

Fri 25    77.6 0.31

85 1.26

91.9 0.45 

Sat 26    97.1 0.78

102.5 0.39

110.1 1.22

117.2 0.44 

Sun 27    122.6 0.77

127.9 0.43 

135.3 1.21

142.3 0.39

Mon 28    148 0.82

153.4 0.42 

160.4 1.24

167.1 0.32 

8/10/2019 maths assignment.doc

http://slidepdf.com/reader/full/maths-assignmentdoc 3/6

  Year 11 Mathematics B  Tides and Period Functions

  Assessment 2.2  Name: Troy Rong

Time

Heights of tides

0 18 36 54 72 90 108 126 144 162 180

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

MAPS 1 : A sine cur"e wi## )e used to mode# the data. As the data shown$ the height o tide at &.-h is

(.( and it is 1.' at 1(./h .Thereore$ the height o tide at midnight on the irst day might )e

c#ose to ( so that a sine cur"e is )etter used or mode##ing the data.

 0owe"er$ data dis!#ayed a)o"e con not )e mode##ed as a norma# sine cur"e )ecause theheight

o tide cou#d not arri"e the highest !oint when it was recorded at the end o each day.Thus $

some o the data here need to )e de#eted when the cacu#ation is carring out. The ta)#e o data is

used or maing a gra!h is shown as )e#ow.

Time Ht

Tue 22    3.8 0.04 

10.5 1.46

16.7 0.2 

 

Wed 23    28.4 0.13 

35.3 1.41

41.6 0.31

 

Thu 24    52.9 0.22 

60.1 1.34

Time

Heights of tides

0 18 36 54 72 90 108 126 144 162 180

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

8/10/2019 maths assignment.doc

http://slidepdf.com/reader/full/maths-assignmentdoc 4/6

  Year 11 Mathematics B  Tides and Period Functions

  Assessment 2.2  Name: Troy Rong

66.6 0.4 

 

Fri 25    77.6 0.31

85 1.26

91.9 0.45 

Sat 26   

102.5 0.39

110.1 1.22

117.2 0.44 

Sun 27   

127.9 0.43 

135.3 1.21

142.3 0.39

Mon 28   

153.4 0.42 

160.4 1.24

167.1 0.32 

KAPS 2 :A"erage !eriod o the tide is eua# to the time o the high tide o the #ast day minus the time

o the high tide o the irst day and then di"ided )y num)er o !eriod .

31'(.41(./56'72.8-h

Mean high tide :  31.' 91.191.&91.2'91.2291.2191.25671.&1

Mean #ow tide :

  3(.(9(.1&9(.229(.&19(.&89(.&89(.&2567(.2'

Mean tide #e"e# :

  31.&19(.2'5627(.8

A"erage am!#itude :

  1.&14(.87(./2

MAPS 2 :

y=.81593446806909sin(0.25246912526063x-1.0870826042081)0.47083189584699

! 2=9.724

8/10/2019 maths assignment.doc

http://slidepdf.com/reader/full/maths-assignmentdoc 5/6

  Year 11 Mathematics B  Tides and Period Functions

  Assessment 2.2  Name: Troy Rong

Time

Heights of tides

0 18 36 54 72 90 108 126 144 162 180

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

As dis!#ayed in the introduction$ tides are the rises and a##s o sea #e"e# caused )y the

com)ined eect o rotation o the earth and the gra"itation o the moon and the sun.;t is <ust

#ie the sine or cosine !eriod unctions which ha"e a !eriod im!acted )y the regu#ar changes.

 0owe"er$ changes o tides are aected )y !#enty o actors . Besides rotation o the earth

and the gra"itation o the moon and the sun $ weather a#so has an im!act on the chang o 

tide.Thereore$!eriod unctions can not demonstrate the ru#e#ess changs o tides which are

in#uencede )y weather or some other actors e+act#y.

Assumption : A## o the data was co##ected correct#y.

=uring these days $ weather were a#ways the same.

The correct data is the essentia# condition and unchanged weather wou#d not ini#uence the

 !rediction made )y !eriod unction.

Strengths and limitations:>sing !eriod unctions is an easy way to orecast tendency o tides.;t can he#! to get to now

the tendency o tides so that !#enty o sea accidents can )e !re"entd eectie#y .0owe"er$

 !eriod unctions used or !redictions o tides do not inc#ude weather actor which can gi"e an

8/10/2019 maths assignment.doc

http://slidepdf.com/reader/full/maths-assignmentdoc 6/6

  Year 11 Mathematics B  Tides and Period Functions

  Assessment 2.2  Name: Troy Rong

unoreseen im!act on tides o oceans so that !eo!#e can

not re#y on this way o orecast in dai#y #ie.

Bibliography:www.)om.go".au6oceanogra!hy6tides6MAPS6#d.shtm#

htt!:66en.wii!edia.org6wii6?osine@?osine