Solving a Physics Problem: Sine vs. Cosine Theta

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SUMMARY

The discussion focuses on the application of sine and cosine functions in solving a physics problem related to change in potential energy. The user questions the use of sine theta in the examiner's expression, noting their own derivation leads to 1 - cosine theta. Additionally, they seek clarification on how theta was eliminated from the equation, referencing approximations for small angles where sin theta approximates theta and cos theta approximates 1 - 1/2 theta squared.

PREREQUISITES
  • Understanding of trigonometric functions, specifically sine and cosine.
  • Familiarity with small angle approximations in physics.
  • Basic knowledge of potential energy concepts.
  • Ability to manipulate algebraic expressions in physics equations.
NEXT STEPS
  • Study the derivation of potential energy expressions using trigonometric functions.
  • Learn about small angle approximations and their applications in physics.
  • Explore the relationship between sine and cosine in various physics contexts.
  • Review algebraic techniques for simplifying equations in physics problems.
USEFUL FOR

Students studying physics, particularly those tackling problems involving trigonometric functions and potential energy calculations.

Faiq
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Homework Statement


Question is provided

The Attempt at a Solution


The required solution is provided

My question is, the examiner have used sine theta in their expression for change in potential. I keep ending up with 1 - cosine theta
Second question is how did they get rid of theta in the proceeding equation
 

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See the left side. For small angles, ##\sin \theta \approx \theta## and ##\cos \theta \approx 1 - \frac 1 2 \theta^2## (sometimes ##\cos \theta \approx 1## is sufficient).
 

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