Solving Trigonometric Equations: What is the Best Way?

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SUMMARY

The discussion focuses on solving trigonometric equations and determining the equivalence of different forms of solutions, such as 2 cos(x) sin(x) and sin(2x). Participants suggest using algebraic identities and value substitution to verify that different expressions yield the same results. Additionally, graphing tools like Wolfram Alpha are recommended for visual comparison of trigonometric functions. The Unit Circle is referenced as a foundational concept for understanding the periodic nature of sine functions.

PREREQUISITES
  • Understanding of trigonometric identities, specifically double angle formulas.
  • Familiarity with the Unit Circle and its implications on sine and cosine values.
  • Basic graphing skills, particularly with trigonometric functions.
  • Knowledge of value substitution techniques in algebra.
NEXT STEPS
  • Research the derivation and application of the double angle formula for sine.
  • Explore the properties of the Unit Circle in relation to trigonometric functions.
  • Learn how to use graphing tools like Wolfram Alpha for visualizing trigonometric equations.
  • Study various algebraic identities that can simplify trigonometric expressions.
USEFUL FOR

Students, educators, and anyone involved in mathematics, particularly those focused on trigonometry and algebraic problem-solving techniques.

phymatter
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while solving trigonometric equations many times we get answer in different forms depending on the way in which we solve the problem , so what is the best way to ascertain that all the answers are the same ??
pl. help!
 
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Do you mean, that you might get the answer as 2 cos(x) sin(x), or as sin(2x) ?

One thing you could do, besides trying to use algebraic identities to transform one into the other, is plug in some values (for example 0, \pi/12, 2\pi/12, 3\pi/12, \ldots, \pi) or draw the graphs of the two expressions (for example, http://www.wolframalpha.com/input/?i=plot+2+cos(x)+sin(x)+and+sin(2x)).
 
Hi, I hope I got your question right. Due to the nature of trig' functions as seen in the Unit Circle (wiki for more info). so sin30=1/2 but sin150=1/2 as well. The simple identity for this is sinx=a+180k,a
 

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