Exploring Spherical Trig: Applications in Physics

In summary: When we are doing physics, we need to know how to do calculations with triangles on the surface of a sphere. This is where spherical trigonometry comes in. It involves formulas such as the versed sine and haversine, which have practical applications in navigation. If you are in 11th grade and interested in learning more, there are friendly books available on this topic. In summary, spherical trigonometry is a branch of trigonometry that deals with calculations on the surface of a sphere, with practical applications in navigation and other areas of physics. There are friendly books available for those interested in learning more about this topic.
  • #1
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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  • #2
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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  • #3
parshyaa said:
what are its application(mostly in physics)
We live on a sphere.
 
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1. What is spherical trigonometry?

Spherical trigonometry is a branch of mathematics that deals with solving triangles on the surface of a sphere. It involves applying the principles of trigonometry to spherical objects and is commonly used in fields such as astronomy, navigation, and physics.

2. What are some applications of spherical trigonometry in physics?

Spherical trigonometry has various applications in physics, including analyzing the movements of celestial bodies, calculating distances and angles in navigation, and determining the relationship between forces and angles in three-dimensional space.

3. How is spherical trigonometry different from planar trigonometry?

The main difference between spherical trigonometry and planar trigonometry is that while planar trigonometry deals with triangles on a flat surface, spherical trigonometry deals with triangles on the curved surface of a sphere. This means that the rules and equations used in spherical trigonometry are specific to the geometry of a sphere.

4. What are some common formulas used in spherical trigonometry?

Some common formulas used in spherical trigonometry include the law of cosines, the law of sines, and the haversine formula. These formulas can be used to solve for unknown sides and angles in a spherical triangle.

5. How is spherical trigonometry used in real-life situations?

Spherical trigonometry is used in many real-life situations, including determining the position of stars and planets in astronomy, calculating distances and angles in navigation, and analyzing the forces acting on objects in physics. It is also used in the construction of maps and globes, as well as in the design of structures that need to withstand forces from all directions.

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