Understanding the Cofunction Identities in Trigonometry

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Homework Help Overview

The discussion revolves around the cofunction identities in trigonometry, specifically examining the identity 1 - (sin²)x = (cos²)x. Participants are exploring the validity of this identity and its relation to other trigonometric concepts.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are questioning the truth of the identity presented and its connection to cofunction identities. Some suggest using the Pythagorean identity sin²x + cos²x = 1 as a basis for understanding. Others propose a geometric interpretation involving right triangles to derive the identity.

Discussion Status

The discussion is active, with participants offering different perspectives on the identity and its implications. Some guidance has been provided regarding the relationship between the identity and basic trigonometric principles, but there is no explicit consensus on the topic yet.

Contextual Notes

Participants mention the need for further information on trigonometric identities and suggest that basic trigonometry may cover these concepts. There is an acknowledgment of feelings of uncertainty among some participants regarding their understanding.

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Homework Statement



My book is showing 1 - (sin^2)x = (cos^2)x, is this true? If so under what subject do I find more information about this. I found cofunction identities where sin(90° - θ) = cosθ but I'm not sure if that's the same thing.

Homework Equations


The Attempt at a Solution

 
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bobsmith76 said:

Homework Statement



My book is showing 1 - (sin^2)x = (cos^2)x, is this true? If so under what subject do I find more information about this. I found cofunction identities where sin(90° - θ) = cosθ but I'm not sure if that's the same thing.

Homework Equations





The Attempt at a Solution


Just rearrange \sin^2 x + \cos^2 x = 1, which you recently asked about in another thread.
 
bobsmith76 said:
My book is showing 1 - (sin^2)x = (cos^2)x, is this true?
Yes, draw a right triangle and label one of the angles x. Now label each side a, b and c. Ok so what is sin(x) in terms of a,b,c? So what is sin2(x)? Continue this for cos2(x) and you'll see the result holds.

bobsmith76 said:
If so under what subject do I find more information about this.
Basic trigonometry? After being taught about graphing trig functions I believe you're exposed to more trig identities.
 
thanks, i feel stupid, but at least i know the answer
 
bobsmith76 said:
thanks, i feel stupid, but at least i know the answer

Nah being stupid would be not knowing the answer in the exam :wink:
 

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