Around the World: Islands of Biological

WonderKristian Wilks - Pre Calc. 11A - 10/1/12

The Trip• Home: St. Clair Shores, MI– Coordinates: 42.4969° N (42°30’ N), 82.8889° W (82°53’ W)

• Destination 1: Santa Cruz Island, Galapagos– Coordinates: 1.3861° N (1°23’ N), 91.9197° W (91°49’ W)

• Destination 2: Antananarivo, Madagascar– Coordinates: 18.9386° S (18°56’ S), 47.5214° E (47°31’ E)

• Destination 3: Sipadan Island, Malaysia– Coordinates: 4.1147° N (4°7’ N), 118.6288° E (118°38’ E)

Equations Used• Spherical Law of Cosines– cos(n) = cos(a)*cos(b) + sin(a)*sin(b)*cos(N)

• Arc Length of Circle– Distance = (n/360)*2*pi*radius of Earth• n is an angle• Radius of Earth = 3960 miles

1st Trip – Santa Cruz Island, Galapagos

Why Santa Cruz Island, Galapagos?

Santa Cruz Island is the main town of the Galapagos. Like the rest of the Galapagos, it is home to unique and exotic plants and animals which cannot be found anywhere on Earth. Imagine being able to walk along side amazing animals such as tortoises while exploring the island. The ocean view along with the natural surroundings make for beautiful scenery that cannot be matched as well. It is an amazing place for those who love wild life and for those who love the mysteries that life holds.

1st Trip – Calculations

Distance 1: St. Clair Shores, MI (S) to Santa Cruz Island, Galapagos (G)

89°60’ - 1°23’s = 88°37’

89°60’ - 42°30’g = 47°30’

1st Trip – Calculations

91°49’ - 82°53’ N = 8°56’

cos n = cos(s)*cos(g)+sin(s)*sin(g)*cos(N)cos n = cos(47°30’)*cos(88°37’)+sin(47°30’)*sin(88°37’)*cos(8°56’)

cos n = 0.744503299071n = 41.8835461944°

Distance 1 = (n/360)*2*pi*rDistance 1 = (41.8835461944 /360)*2*pi*3960 milesDistance 1 = 2,895 miles

2nd Trip – Antananarivo, Madagascar

Why Antananarivo, Madagascar?

Antananarivo is the capital of Madagascar and the center of human life here. Though the city itself is not the focus, the island of Madagascar is filled with exotic animals and plants that will amaze the minds of the tourists who travel there. The lemurs and strange reptiles that call Madagascar home are the main reason to visit providing experiences and sights that are unparalleled by any other place on Earth.

2nd Trip – Calculations

Distance 2: Santa Cruz Island, Galapagos (G) to Antananarivo, Madagascar (M)

89°60’ + 18°56’g = 108°56’

89°60’ - 1°23’m = 88°37’

2nd Trip – Calculations

91°49’ + 47°31’N = 139°20’

cos n = cos(g)*cos(m)+sin(g)*sin(m)*cos(N)cos n = cos(88°37’)*cos(108°56’)+sin(88°37’)*sin(108°56’)*cos(139°20’)

cos n = -0.725177359314n = 136.483604035°

Distance 2 = (n/360)*2*pi*rDistance 2 = (136.483604035 /360)*2*pi*3960 milesDistance 2 = 9,433 miles

3rd Trip – Sipadan Island, Malaysia

Why Sipadan Island, Malaysia?

Sipadan Island is off the coast of Borneo and belongs to Malaysia. Although the island itself is fascinating, the real reason to visit is the sea life surrounding the islands. Taking a dive down around the reefs provides for an up close view of the stunning sea life that is unique to the area. Imagine being able to swim along side sea turtles and other amazing fish while viewing the beautiful reefs below! It is the perfect way to get away from home and unwind!

3rd Trip – Calculations

Distance 3: Antananarivo, Madagascar (M) to Sipadan Island, Malaysia (I)

89°60’ - 4°7’m = 85°53’

89°60’ +18°56’i =108°56’

3rd Trip – Calculations

118°38’ - 47°31’ N = 71°7’

cos n = cos(m)*cos(i)+sin(m)*sin(i)*cos(N)cos n = cos(108°56’)*cos(85°53’)+sin(108°56’)*sin(85°53’)*cos(71°7’)

cos n = 0.328765647938n = 70.8061275329°

Distance 3 = (n/360)*2*pi*rDistance 3 = (70.8061275329 /360)*2*pi*3960 milesDistance 3 = 4,894 miles

4th Trip – Back Home

4th Trip – Calculations

Distance 4: Sipadan Island, Malaysia (I) to St. Clair Shores, MI (S)

89°60’ - 42°30’i = 47°30’

89°60’ - 4°7’s = 85°53’

4th Trip – Calculations

360- (118°38’+82°53’)N = 158°29’

cos n = cos(i)*cos(s)+sin(i)*sin(s)*cos(N)cos n = cos(85°53’)*cos(47°30’)+sin(85°53’)*sin(47°30’)*cos(158°29’)

cos n = -0.635685246581n = 129.470826473°

Distance 3 = (n/360)*2*pi*rDistance 3 = (129.470826473 /360)*2*pi*3960 milesDistance 3 = 8,948 miles

Picture Sources• Picture of Earth:

– http://www.google.com/imgres?q=picture+of+earth&um=1&hl=en&safe=active&sa=N&biw=1092&bih=499&tbm=isch&tbnid=j8-LMYuOxLVKxM:&imgrefurl=http://blenderartists.org/forum/showthread.php%3F229511-Clouds-From-the-view-of-space&docid=zWazXI2pLPreaM&imgurl=http://gkbsolarsystem.wikispaces.com/file/view/earth2_medium.jpg/116480707/earth2_medium.jpg&w=1440&h=1540&ei=zKRoUIK1B6XzyAHKhIGICA&zoom=1&iact=hc&vpx=96&vpy=123&dur=797&hovh=232&hovw=217&tx=133&ty=138&sig=117730032865579301503&page=2&tbnh=148&tbnw=128&start=12&ndsp=16&ved=1t:429,r:5,s:12,i:132

• Picture of Santa Cruz Tortoise:– http://www.google.com/imgres?

q=santa+cruz+island+galapagos&start=101&um=1&hl=en&safe=active&sa=N&biw=1092&bih=499&tbm=isch&tbnid=y0btuWZpH0Be1M:&imgrefurl=http://matthewmeierphoto.photoshelter.com/image/I0000DWN3GoQDWZU&docid=KXZCwCFPvNz3JM&imgurl=http://cdn.c.photoshelter.com/img-get/I0000DWN3GoQDWZU/s/750/750/galapagos-giant-tortoise-wild-013065.jpg&w=750&h=498&ei=wJ1oUMfVHcaJywG5zYG4BQ&zoom=1&iact=rc&dur=310&sig=117730032865579301503&page=8&tbnh=153&tbnw=215&ndsp=15&ved=1t:429,r:12,s:101,i:93&tx=135&ty=33

• Picture of Madagascar Lemur:– http://www.google.com/imgres?

q=madagascar&um=1&hl=en&safe=active&biw=1092&bih=499&tbm=isch&tbnid=_ztuCUzrlwVL3M:&imgrefurl=http://animals.howstuffworks.com/mammals/lemurs-live-in-madagascar1.htm&docid=3gKl6-K4zcFVkM&imgurl=http://static.ddmcdn.com/gif/lemurs-live-in-madagascar-4.jpg&w=400&h=300&ei=_I5oUMq_LomkyQG4zoDADQ&zoom=1&iact=hc&vpx=657&vpy=4&dur=1510&hovh=195&hovw=260&tx=129&ty=60&sig=117730032865579301503&page=5&tbnh=141&tbnw=212&start=61&ndsp=16&ved=1t:429,r:3,s:61,i:280

Picture Sources• Picture of Sipadan Island Sea Turtle:

– http://www.google.com/imgres?q=sipadan+island+malaysia&um=1&hl=en&safe=active&sa=N&rlz=1C1TSNO_enUS463US463&biw=1092&bih=499&tbm=isch&tbnid=yQ1lmhxXFm6nrM:&imgrefurl=http://www.divetrip.com/phot0307e.htm&docid=TcYhEvkzhhRtM&imgurl=http://www.divetrip.com/photos/sipturtle4.jpg&w=640&h=480&ei=bJtoUMONL9KFyQGA0IDACA&zoom=1&iact=hc&vpx=342&vpy=64&dur=1876&hovh=195&hovw=260&tx=147&ty=150&sig=117730032865579301503&page=4&tbnh=144&tbnw=213&start=40&ndsp=13&ved=1t:429,r:1,s:40,i:211

• Picture of St. Clair Shores Nautical Mile Sign:– http://www.google.com/imgres?q=St.

+clair+shores+michigan&um=1&hl=en&safe=active&sa=N&biw=1092&bih=499&tbm=isch&tbnid=zSIbus1PMWQrsM:&imgrefurl=http://localism.com/mi/saint_clair_shores/the_nautical_mile&docid=W0rP28ys13SOSM&imgurl=http://localism.com/system/s3_buckets/localism-production-image-store/photo_c5191b9da1ae4497cd5c0d10b82b6d950d3e46c7a528caaeb6a6bfdcb8141bd3.jpg&w=1024&h=768&ei=fJ1oUJPDDcHIyQGM6YGAAQ&zoom=1&iact=rc&dur=1&sig=117730032865579301503&page=1&tbnh=143&tbnw=176&start=0&ndsp=10&ved=1t:429,r:5,s:0,i:89&tx=242&ty=320

THE END!