Mathematics
BREE12779:

Earth has been charted with vertical and horizontal lines so that points can be named with coordinates. The horizontal lines are called latitude lines. The equator is latitude line 0. Parallel lines are numbered up to pi/2 to the north and to the south. If we assume Earth is spherical, the length of any parallel of latitude is equal to the circumference of a great circle of Earth times the cosine of the latitude angle. a. The radius of earth is about 6400 kilometers. Find the circumference of a great circle. b. Write an equation for the circumference of any latitude circle with angle (theta) c. Which latitude circle has a circumference of about 3593 kilometers? d. What is the circumference of the equator?

Vocaloid:

a) the great circle of a sphere is the largest circle that can be drawn enclosing a sphere. on Earth this is the Equator. you can treat the great circle as a circle with radius = 6400km formula for circumference = 2 * pi * r

Vocaloid:

b) a latitude circle circumference, as defined by the problem, is the circumference of the great earth (from part a) multiplied by the cos of the latitude angle they give you latitude angle = θ so just multiply the great circle circumference by cos(θ)

Vocaloid:

c) you can use the formula (latitude circle circumference) = (great circle circumference)(cosθ) from part b to solve for θ

Vocaloid:

d) as I stated earlier the great circle of Earth is the equator so your sol'n should be the same as what you got from a) if they want you to use the formula from part b) you can define θ at the Equator as θ = 0 degrees and solve that way