What is the distance, measured along a great circle, between locations at #(34^o N, 34^o W) and (34^ S, 34^o E)#?

Answer 1

#10360# km #= 10.36# Mm, for 4-sd rounding

There are negatives for west longitudes and south latitudes.

The position vectors to the spherical-polar coordinates

places

#P(6371, 34^o, -34^o) and Q(9371, -34^o, 34^o)# from the center O

of the planet Earth are

#OP=6371( cos 34° cos(- 34°), cos 34° sin(- 34^o°), sin 34°# and
#OQ=6371( cos(- 34°) cos 34°, cos(- 34°) sin 34°, sin(- 34°)#,

For unit vectors #n_(OP) and n_(OQ), omit the factor 6371 km (mean

the Earth's radius) in these normal directions.

The great-circle arc PQ at the center subtends the angle

#alpha=arc cos(n_(OP)·n_(OQ))#
#=arc cos (cos^4 34°-cos^2 34° sin^2 34°-sin^2 34°)#
#=arc cos(cos^2 34° cos 68°-sin^2 34°)#
#=93.16°#

The great-circle arc distance, expressed in radians (PQ = 6371 X alpha),

#=6371(93.16/180)\pi)# km
#=10360# km #= 10.36# Mm, for 4-sd rounding
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Answer 2

The distance, measured along a great circle, between locations at (34° N, 34° W) and (34° S, 34° E) is approximately 14,832 kilometers.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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