Trig Help: Deriving a Friction Equation from Circular Motion Example

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SUMMARY

The discussion focuses on deriving a friction equation from a circular motion example, specifically addressing the transition from sine and cosine functions to tangent functions in the equation. The user references a specific problem from Batesville's physics site and seeks clarification on the mathematical steps involved. The key insight provided is the suggestion to multiply the top and bottom of the equation by 1/cosθ to facilitate the derivation process.

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  • Understanding of circular motion principles
  • Familiarity with trigonometric identities, particularly sine, cosine, and tangent
  • Basic algebraic manipulation skills
  • Knowledge of friction in physics contexts
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  • Study the derivation of friction equations in circular motion scenarios
  • Learn about trigonometric identities and their applications in physics
  • Explore the concept of banked curves and their relation to friction
  • Review examples of similar physics problems involving circular motion and friction
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Students studying physics, particularly those focusing on mechanics and circular motion, as well as educators seeking to enhance their teaching methods in these topics.

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Homework Statement



Well I'm following an example problem on this site:
http://www.batesville.k12.in.us/physics/PhyNet/Mechanics/Circular Motion/banked_with_friction.htm
I just need some help on the derivation math. I'll just host the image below.

Homework Equations


This is the problem equation:
http://img105.imageshack.us/img105/3449/frictioneqn4.th.gif

On the last line when it goes from sines and cosines to tangants I can't follow what the person did.


The Attempt at a Solution



I'm assuming he used some type of trig Identity but I can't find one that is apt. I thinking it's a sum/difference trig identity but it just doesn't help. What could he be doing?

Any help at all is GREATLY apperciated!

Thanks
 
Last edited by a moderator:
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Multiply top and bottom by 1/cosθ
 

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