Solving Trigonometric Equations: Divide by Cosine

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Homework Help Overview

The discussion revolves around solving the trigonometric equation sin(x) + cos(x) = 0, which involves manipulating trigonometric identities and exploring potential solutions.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the implications of dividing by cos(x) and the identities that may arise from this operation. There is also an exploration of rewriting the equation in terms of a quadratic form by substituting sin(x) with a variable.

Discussion Status

The discussion is active with participants offering different approaches to the problem. Some guidance has been provided regarding the manipulation of the equation and the potential use of quadratic solutions, but no consensus or final solution has been reached.

Contextual Notes

There is an acknowledgment of the original poster's uncertainty about the next steps after deriving sin(x) = sin^2(x) - 1, and the implications of dividing by cos(x) are under consideration.

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Homework Statement


sinx + cosx = 0

Homework Equations


N/A

The Attempt at a Solution



sinx + cosx = 0

sinx = -cosx
sinx = (+/-) sqrt(sin^2x - 1)
(sinx)^2 = (+/-) sqrt(sin^2x - 1)^2
sinx = sin^2x - 1

Not really too sure what to do from here on.

The answer is 3[tex]\pi[/tex]/4 and 7[tex]\pi[/tex]/4.

I appreciate the help, thanks in advance.
 
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[tex]sin x = -\cos x[/tex]

Divide by cosx, what identity do you get?
 
Or, since you have gone to all the work of getting to [itex]sin(x)= sin^2(x)- 1[/tex], let y= sin(x) and rewrite it as y^2- y- 1= 0. solve that quadratic equation for y and then solve sin(x)= y.[/itex]
 
Last edited by a moderator:
Divide by cosx, what identity do you get?

Thank you for the assistance, I can't believe I missed that!
 

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