How Do You Isolate A in the Equation n=sin[(A+B)/2]/sin(B/2)?

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SUMMARY

The discussion focuses on isolating variable A in the equation n=sin[(A+B)/2]/sin(B/2). The user successfully transformed the equation to 2nsin(B/2) = sin(A+B) and recognized that sin(A+B) can be expanded to sinAcosB + cosAsinB. However, they seek further assistance in simplifying or solving for A, indicating a need for deeper insights into trigonometric identities and manipulations.

PREREQUISITES
  • Understanding of trigonometric identities, specifically the sine addition formula.
  • Familiarity with algebraic manipulation of equations.
  • Knowledge of the sine function and its properties.
  • Basic skills in solving equations involving trigonometric functions.
NEXT STEPS
  • Study the sine addition formula in detail to understand its applications.
  • Learn about the half-angle identities, particularly sin(B/2).
  • Explore methods for isolating variables in trigonometric equations.
  • Practice solving similar trigonometric equations to enhance problem-solving skills.
USEFUL FOR

Students studying trigonometry, educators teaching mathematical concepts, and anyone looking to improve their skills in solving trigonometric equations.

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Homework Statement



given this formula, i have to solve for A

n=sin[(A+B)/2]/sin(B/2)


Homework Equations





The Attempt at a Solution



Heres how far I got

2nsin(B/2) = sin(A+B) i know this can expand out to
=sinAcosB + cosAsinB but this isn't much help. Anyone got a suggestion
 
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joemama69 said:

Homework Statement



given this formula, i have to solve for A

n=sin[(A+B)/2]/sin(B/2)


Homework Equations





The Attempt at a Solution



Heres how far I got

2nsin(B/2) = sin(A+B) i know this can expand out to
=sinAcosB + cosAsinB but this isn't much help. Anyone got a suggestion

Made me think of the interweb

sin(\frac{B}{2}) = sin(\frac{B}{2}) = \frac{1-cos(B)}{2}
 
Last edited:

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