Does cos + sin always equal 0?

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Discussion Overview

The discussion revolves around the question of whether the sum of cosine and sine functions can equal zero. Participants explore various interpretations of the question, including specific cases and general properties of the functions involved.

Discussion Character

  • Debate/contested

Main Points Raised

  • One participant questions if the original inquiry is about the general case of cos + sin equating to zero or specific instances involving arguments of the functions.
  • Another participant emphasizes that sine and cosine are functions and do not have fixed values, suggesting a need for clarification on the context of the question.
  • A different participant provides a specific example where sin(2n pi) + cos[(pi/2) + n pi] equals zero, indicating that there are cases where the sum can be zero.
  • One participant interprets the question as asking if cos(x) + sin(x) = 0, leading to the condition that cos(x) = -sin(x), which implies cot(x) = -1.
  • Another participant humorously suggests that the question may indeed relate to calculus, referencing the maximum and minimum values of the function sin(x) + cos(x) and noting its continuity.
  • One participant provides a definitive answer stating that cos + sin does not equal zero in general.
  • A later reply reminds participants of the Pythagorean identity, cos²(x) + sin²(x) = 1, which may have been confused with the original question.

Areas of Agreement / Disagreement

Participants express differing views on the interpretation of the question, with some asserting that cos + sin cannot equal zero in general, while others provide specific examples where it can. The discussion remains unresolved regarding the generality of the claim.

Contextual Notes

Participants have not reached a consensus on the interpretation of the original question, and there are assumptions about the arguments of the sine and cosine functions that remain unaddressed.

Ry122
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does cos + sin = 0?
 
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cos + sin can never be equal to anything other than cos + sin. sin and cos are just functions. Neither has a "value" as such.

Do you want to if sin(somevalue1) + cos(somevalue2) = 0?
 
Ry122 said:
does cos + sin = 0?

like neutrino said cos + sin have no meaning. But if we get let's say

sin(2n pi)+ cos[(pi/2)+n pi] =0, and there are more samples like this. if this is what you meant at first place?
 
did you mean [tex]cosx+sinx=0[/tex] ?
[tex]\mbox{for the above to be true},\\ cosx=-sinx \\ \Rightarrow cotx=-1[/tex] (or [tex]sinx=0[/tex] but this does not hold for that.)
 
Please only post calculus questions in this forum.
 
ChaoticLlama said:
Please only post calculus questions in this forum.
LOL,this may well be calculus...
[tex]Max(sinx+cosx)= \sqrt{2}[/tex]
[tex]Min(sinx+cosx)= -\sqrt{2}[/tex]
Since they function is continuous, it must have x such that f(x)=0
 
To OP: Short answer. No.
 
Wait up, perhaps you got confused with this:

[tex]\cos^2 x + \sin^2 x = 1[/tex]
 

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