Intrinsic Equation: Showing tan φ/2 = e^s

Thread starter kingOFleo
Start date Jun 13, 2007

In summary, an intrinsic equation is a mathematical relationship that describes a geometric object or physical phenomenon using only its inherent properties, without reference to any external coordinate system. In the specific equation tan φ/2 = e^s, tan φ/2 represents the rotation angle and e^s represents the spin magnitude. The intrinsic equation is useful in scientific research, particularly in fields such as physics and engineering, as it allows for accurate descriptions and analysis of rotations and spins without being constrained by a specific coordinate system. It can be applied to any object or phenomenon that involves rotation and spin, from subatomic particles to celestial bodies. While there are various methods for solving intrinsic equations depending on the specific equation and context, it typically involves using mathematical techniques such as

Jun 13, 2007

kingOFleo

For the curve with equation siny =e^x, where s is measured from the point(0,pi/2),show that e^s =tan?/2.
tan?/2 where?=phi
hlp me please
contact me nikvoodoo@gmail.com

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Jun 13, 2007

Office_Shredder

Staff Emeritus

Science Advisor

Gold Member

You definitely haven't given enough information... how are s and phi related to y and x?

Jun 14, 2007

kingOFleo

i also can't understand this but this came in my exam
please try to this
hlp me

1. What is an intrinsic equation?

An intrinsic equation is a mathematical relationship that is independent of any coordinate system or external reference frame. It is a way of describing a geometric object or a physical phenomenon using only the properties inherent to that object or phenomenon.

2. What does tan φ/2 = e^s represent in the intrinsic equation?

In this intrinsic equation, tan φ/2 represents the tangent of half the angle of rotation, while e^s represents the exponential function of the spin magnitude. Together, they describe the rotation and spin of an object in a way that is independent of any external reference frame.

3. How is the intrinsic equation useful in scientific research?

The intrinsic equation is particularly useful in fields such as physics and engineering, where precise descriptions of rotations and spins are needed. By using this equation, scientists can accurately describe and analyze the behavior of objects without being limited by the constraints of a specific coordinate system.

4. Can the intrinsic equation be applied to any type of object or phenomenon?

Yes, the intrinsic equation can be applied to any object or phenomenon that involves rotation and spin. This includes everything from subatomic particles to celestial bodies.

5. Is there a specific method for solving intrinsic equations?

There are different methods for solving intrinsic equations depending on the specific equation and context. In general, it involves using mathematical techniques such as calculus and linear algebra to manipulate the equation and solve for the unknown variables.