How Do You Solve These Trigonometric Equations for Relative Motion?

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Discussion Overview

The discussion revolves around solving a set of trigonometric equations related to relative motion. Participants explore methods for manipulating the equations and seek guidance on solving for the unknowns involved.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant presents two equations involving trigonometric functions and expresses uncertainty about how to proceed with solving them.
  • Another participant suggests squaring the equations as a potential method for finding a solution.
  • A different participant recommends substituting cos45 and sin45 with sqrt(2)/2, assuming the angles are in degrees.
  • One participant mentions having squared the equations but is unsure of the next steps and asks for methods to solve them.
  • Another participant inquires about identities related to the sum of the squares of sine and cosine functions, hinting at possible approaches to the problem.
  • A later reply outlines a method involving substitution of one equation into another to reduce the number of unknowns, suggesting trial and error for finding solutions.

Areas of Agreement / Disagreement

Participants express various methods and approaches to solving the equations, but there is no consensus on a single method or solution. Uncertainty remains regarding the best way to proceed.

Contextual Notes

Participants have not fully resolved the mathematical steps involved in solving the equations, and there are dependencies on the definitions and assumptions made about the angles and variables.

Who May Find This Useful

Students or individuals interested in trigonometric equations, relative motion problems, or those seeking collaborative problem-solving approaches in mathematics.

weedannycool
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Homework Statement



i have 2 equations:

400cos \varthetaa = 300 + Vacos45

and

400sin \varthetaa = Vasin45

Homework Equations





The Attempt at a Solution



i have no clue, maybe square it.

thanks
 
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Hi weedannycool! :wink:
weedannycool said:
… maybe square it.

Yes, of course …

what do you get? :smile:
 
Also, you should replace cos45 and sin45 by sqrt(2)/2. I'm assuming the angles are in degrees.

One other thing. Instead of starting a new thread for essentially the same (but corrected) problem, you should continue the old thread, putting in the corrected set of equations.
 
right so i have the to equations squared. not positive with what i should to next though. is there a method for solving these.

thanks for the help so far
 
Do you know any identities involving the sum of the squares of the sine and cosine functions?
 
Mark44's approach replacing sin45 and cos45 with sqrt(2)/2 seems the most straight forward approach. You have 2 equations with 2 unknowns, theta-a and Va. The expression with Va*sqrt(2)/2 in the second equation can be substituted into the first equation. You are left with one equation with one unknown, theta-a. Trial and error to find theta-a. Plug theta-a into either equation to find Va. Theta-a will be in degrees, Va won't be.
 
thanks guys. relative motion is a blast.
 

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