How Do You Solve These Trigonometric Equations for Relative Motion?

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SUMMARY

The discussion focuses on solving two trigonometric equations related to relative motion: 400cos(θ-a) = 300 + Vacos(45) and 400sin(θ-a) = Vasin(45). Participants suggest substituting cos(45) and sin(45) with √2/2 to simplify the equations. The method involves substituting the expression for Va from the second equation into the first, resulting in a single equation with one unknown, θ-a. The final step is to use trial and error to determine θ-a and subsequently calculate Va.

PREREQUISITES
  • Understanding of trigonometric identities, specifically for sine and cosine functions.
  • Familiarity with solving systems of equations with two variables.
  • Knowledge of relative motion concepts in physics.
  • Basic algebra skills for manipulating equations and performing substitutions.
NEXT STEPS
  • Study trigonometric identities, particularly the Pythagorean identity involving sine and cosine.
  • Learn methods for solving systems of equations, including substitution and elimination techniques.
  • Explore relative motion problems in physics to understand practical applications of these equations.
  • Practice solving trigonometric equations using numerical methods or graphing techniques.
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and relative motion, as well as anyone looking to enhance their skills in solving trigonometric equations.

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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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