Solving Trig Related Physics Problem: Step by Step Guide

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SUMMARY

The discussion focuses on solving a physics problem involving trigonometric functions, specifically the equation 19.6m + 800m * cos(Z)^2 = 2,000m * sqrt(1 - cos(Z)^2) * cos(Z). The user seeks clarification on how to transition from this equation to the expanded form 384m^2 + 31,360m^2 * cos(Z)^2 + 640,000m^2 * cos(Z)^4 = 4,000,000m^2 * cos(Z)^2 - 4,000,000m^2 * cos(Z)^4. The solution involves squaring both sides of the equation, which leads to the derived terms, with a noted approximation of 384.16m^2.

PREREQUISITES
  • Understanding of trigonometric identities, particularly cos(Z) and its properties.
  • Familiarity with algebraic manipulation of equations.
  • Knowledge of physics concepts related to motion and forces.
  • Ability to work with square roots and squares in mathematical expressions.
NEXT STEPS
  • Study the derivation of trigonometric identities and their applications in physics problems.
  • Learn about the process of squaring equations and how it affects the terms involved.
  • Explore examples of physics problems that require the use of trigonometric functions.
  • Investigate the relationship between trigonometric functions and quadratic equations.
USEFUL FOR

Students in physics, mathematics enthusiasts, and educators looking to deepen their understanding of trigonometric applications in physics problems.

rockytriton
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I'm trying to solve a physics problem with some trig in it. I'm looking at a solution but I'm not understanding where it gets from one step to another.

I understand it up to this point:

19.6m + 800m * cos(Z)^2 = 2,000m * sqr(1 - cos(Z)^2) * cos(Z)

But I don't understand how they get from that to:

384m^2 + 31,360m^2 * cos(Z)^2 + 640,000m^2 * cos(Z)^4 =
4,000,000m^2 * cos(Z)^2 - 4,000,000m^2 * cos(Z)^4

Is this some kind of crazy trig trick that I don't know about?
 
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rockytriton said:
I'm trying to solve a physics problem with some trig in it. I'm looking at a solution but I'm not understanding where it gets from one step to another.

I understand it up to this point:

19.6m + 800m * cos(Z)^2 = 2,000m * sqr(1 - cos(Z)^2) * cos(Z)

But I don't understand how they get from that to:

384m^2 + 31,360m^2 * cos(Z)^2 + 640,000m^2 * cos(Z)^4 =
4,000,000m^2 * cos(Z)^2 - 4,000,000m^2 * cos(Z)^4

Is this some kind of crazy trig trick that I don't know about?


Raise both sides of the equation to the second power and here you are (approximately, should have been 384.16m^2).
 

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