Every point on Earth can be represented by a three-dimensional vector. The vector's starting point is at the center of Earth. To calculate the unit vectors corresponding to each of your locations, apply these formulas: v = (x, v.:), where the following applies: x = cos(latitude) cos(longitude) y= cos(latitude) sin(longitude) := sin(latitude) The latitude and longitude for Miami Florida and Anchorage Florida in degrees are: ne of Location mi Florida horage, Alaska Latitude 25.7671° N 61.2181° N Longitude 80.1918° W 149.9003° W ***Use a Negative sign for southern latitudes or western longitudes ***Use a Positive sign for northern latitudes or eastern longitudes. 1: Calculate the corresponding three - dimensional unit vector for each location. Use 5 decimal places for all
Every point on Earth can be represented by a three-dimensional vector. The vector's starting point is at the center of Earth. To calculate the unit vectors corresponding to each of your locations, apply these formulas: v = (x, v.:), where the following applies: x = cos(latitude) cos(longitude) y= cos(latitude) sin(longitude) := sin(latitude) The latitude and longitude for Miami Florida and Anchorage Florida in degrees are: ne of Location mi Florida horage, Alaska Latitude 25.7671° N 61.2181° N Longitude 80.1918° W 149.9003° W ***Use a Negative sign for southern latitudes or western longitudes ***Use a Positive sign for northern latitudes or eastern longitudes. 1: Calculate the corresponding three - dimensional unit vector for each location. Use 5 decimal places for all
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![Part 2: Find the angle 0 between your 2 vectors. Show your work and final answer. Make sure your
final angle 0 is in radians not degrees. Use 5 decimal places in all your calculations.
Part 3: Find the distance between the two locations to the nearest mile. Show your work and final answer
with units.
Remember your angle needs to be in radians when you compute arc length.
Although Earth is not a perfect sphere, assume that it is for the purposes of this
portfolio and use the formula for the arc length of a segment of a great circle on a
sphere, s = r0, to find the distance between your two locations. In this case, r is the
radius of Earth, which is approximately 3,963.2 miles. Find the distance between
your two locations.
Part 5: Look up the actual distance between the two cities (include your source). Calculate the percentage of
error in your calculation and comment on how accurate it is and possible sources of error. Consider why
your online source might be less or more accurate than your calculation](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb5ce8f49-e83b-45d5-bdba-74aac31b7d31%2Fdbcfcbb2-a32a-4520-99b1-e203c26e1c0a%2Fh8ukvsi_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Part 2: Find the angle 0 between your 2 vectors. Show your work and final answer. Make sure your
final angle 0 is in radians not degrees. Use 5 decimal places in all your calculations.
Part 3: Find the distance between the two locations to the nearest mile. Show your work and final answer
with units.
Remember your angle needs to be in radians when you compute arc length.
Although Earth is not a perfect sphere, assume that it is for the purposes of this
portfolio and use the formula for the arc length of a segment of a great circle on a
sphere, s = r0, to find the distance between your two locations. In this case, r is the
radius of Earth, which is approximately 3,963.2 miles. Find the distance between
your two locations.
Part 5: Look up the actual distance between the two cities (include your source). Calculate the percentage of
error in your calculation and comment on how accurate it is and possible sources of error. Consider why
your online source might be less or more accurate than your calculation
![Every point on Earth can be represented by a three-dimensional vector. The
vector's starting point is at the center of Earth.
To calculate the unit vectors corresponding to each of your locations, apply these
formulas:
v= (x, y. :), where the following applies:
x= cos(latitude) cos(longitude)
y = cos(latitude) - sin(longitude)
:= sin(latitude)
The latitude and longitude for Miami Florida and Anchorage Florida in degrees are:
Name of Location
Miami Florida
Anchorage, Alaska
Latitude
25.7671° N
61.2181° N
Longitude
80.1918° W
149.9003° W
***Use a Negative sign for southern latitudes or western longitudes
***Use a Positive sign for northern latitudes or eastern longitudes.
Part 1: Calculate the corresponding three - dimensional unit vector for each location.
Use 5 decimal places for all
y- coordinate
cos(latitude)*cos{longitude) cos(latitude)*sin(longitude) sin(latitude)
Location
x- coordinate
z- coordinate
<x, y, 2>
Miami,
Florida
Anchorage,
Alaska](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb5ce8f49-e83b-45d5-bdba-74aac31b7d31%2Fdbcfcbb2-a32a-4520-99b1-e203c26e1c0a%2F5f2tb3i_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Every point on Earth can be represented by a three-dimensional vector. The
vector's starting point is at the center of Earth.
To calculate the unit vectors corresponding to each of your locations, apply these
formulas:
v= (x, y. :), where the following applies:
x= cos(latitude) cos(longitude)
y = cos(latitude) - sin(longitude)
:= sin(latitude)
The latitude and longitude for Miami Florida and Anchorage Florida in degrees are:
Name of Location
Miami Florida
Anchorage, Alaska
Latitude
25.7671° N
61.2181° N
Longitude
80.1918° W
149.9003° W
***Use a Negative sign for southern latitudes or western longitudes
***Use a Positive sign for northern latitudes or eastern longitudes.
Part 1: Calculate the corresponding three - dimensional unit vector for each location.
Use 5 decimal places for all
y- coordinate
cos(latitude)*cos{longitude) cos(latitude)*sin(longitude) sin(latitude)
Location
x- coordinate
z- coordinate
<x, y, 2>
Miami,
Florida
Anchorage,
Alaska
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