Cos^2+Sin^2 = 1 even with coefficients?

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  • Thread starter Thread starter Tyrion101
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    Coefficients even
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Discussion Overview

The discussion revolves around the application of the trigonometric identity cos²θ + sin²θ = 1 in the context of expressions that include coefficients. Participants explore whether coefficients can be factored out and how this affects the identity's validity.

Discussion Character

  • Technical explanation, Conceptual clarification, Homework-related

Main Points Raised

  • Some participants inquire about the applicability of the basic trigonometric identity when coefficients are involved.
  • One participant suggests that coefficients can be factored out in certain cases, specifically when the expression is of the form x * cos²θ + x * sin²θ = x.
  • Another participant argues that in different scenarios, such as y * cos²θ + x * sin²θ, the identity does not hold in the same way.
  • An example is provided where 5cos²x + 5sin²x is discussed, questioning whether the terms are treated as separate variables or the same due to the coefficient.
  • Participants express uncertainty about how the identity interacts with coefficients and seek clarification through examples.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the treatment of coefficients in relation to the trigonometric identity. Multiple views are presented regarding when and how the identity can be applied with coefficients.

Contextual Notes

Some limitations include potential misunderstandings of the term "coefficient" and the need for clearer examples to illustrate the points being discussed.

Tyrion101
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I have a problem that works out to this s, but with a coefficient, what do I do with it from this point?
 
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If you have a problem, please post it in one of the HW forums and use the HW template. As it stands, it is unclear what you are trying to find.
 
The basic trig identity I was merely asking if it applied also when there were coefficients, can you factor them out if you realize it is the most basic of identities?
 
Tyrion101 said:
The basic trig identity I was merely asking if it applied also when there were coefficients, can you factor them out if you realize it is the most basic of identities?

If you are asking does x * cos2θ + x * sin2θ = x, then the answer is yes.

If you are asking does y * cos2θ + x * sin2θ = y + x, then the answer is no.

Remember, the normal rules of algebra in making the proper simplification.
 
Tyrion101 said:
The basic trig identity I was merely asking if it applied also when there were coefficients, can you factor them out if you realize it is the most basic of identities?

Please give an example, because you're misusing the term "coefficient".
 
An example: 5Cos^2x +5Sin^2x, I'm on my iPad and don't have access to theta, so just assume it's there. Are these treated as separate variables or the same since if you took away the 5 it would equal 1?
 
That's equivalent to one of the results Steamking posted.

Try factoring out the number 5, and then apply the rule that you know.
 
Ok thanks! I just wasn't sure how that rule worked with this kind of problem.
 

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