I When is spherical trigonometry introduced and how does it apply to physics?

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Spherical trigonometry is typically introduced in high school or early college, often in courses related to geometry or physics. Its applications are significant in fields like navigation, where formulas such as the haversine are essential for calculating distances on a sphere. The discussion highlights a specific interest in the versed sine formula and its relevance to navigation. Participants note that while the subject can be challenging, its practical uses in real-world scenarios are important. Understanding spherical trigonometry is crucial for grasping concepts in physics and navigation.
parshyaa
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  • When do we learn about spherical trigonometry and what are its application(mostly in physics)
  • I have read a formula named versed sine = 1- cos(θ) in the trigonometry book by S.L loney, I tried it on google to know more about it and the research made me shocked, haversine(half of versed sine) formula is used for navigation, and it comes under spherical trigonometry, therefore I want to know more about it , I am in 11th grade, is there any friendly book on this topic which can be friendly for me. Thanks.
 
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parshyaa said:
  • When do we learn about spherical trigonometry and what are its application(mostly in physics)
  • I have read a formula named versed sine = 1- cos(θ) in the trigonometry book by S.L loney, I tried it on google to know more about it and the research made me shocked, haversine(half of versed sine) formula is used for navigation, and it comes under spherical trigonometry, therefore I want to know more about it , I am in 11th grade, is there any friendly book on this topic which can be friendly for me. Thanks.
I'm sure it very likely has practical applications but I swear, when I took it many years ago, I was CONVINCED that its primary application was to give me a headache.
 
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parshyaa said:
what are its application(mostly in physics)
We live on a sphere.
 
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Thread 'Trigonometry problem of interest'

Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
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