Simplifying Core 3 Compound Angles

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Homework Help Overview

The discussion revolves around simplifying the expression cosBcosB + sinBsinB, which relates to trigonometric identities and their foundational definitions. Participants are exploring the connection between this expression and the Pythagorean theorem, as well as the definitions of sine and cosine.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are questioning the reasoning behind the expression simplifying to 1, with some exploring the definitions of sine and cosine in the context of right-angled triangles and the unit circle.

Discussion Status

The discussion is actively exploring various interpretations of sine and cosine, particularly in relation to their definitions and the implications of the Pythagorean theorem. Some participants are seeking clarification on terminology and foundational concepts.

Contextual Notes

There is a mention of potential language barriers affecting understanding, particularly regarding the term "SOHCAHTOA," which may not be familiar to all participants.

CathyLou
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Hi.

Could someone please tell me the method to use to simplify cosBcosB + sinBsinB?

Any help would be really appreciated.

Thank you.

Cathy
 
Last edited:
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Well, isn't that equal to 1??
 
arildno said:
Well, isn't that equal to 1??

Yeah, 1 is the answer in the back of the book. I just do not know why. Could you please explain?

Thank you.

Cathy
 
Well, how was cosine and sine to an angle defined to you in the first place?

Perhaps in terms of right-angled triangles?
 
arildno said:
Well, how was cosine and sine to an angle defined to you in the first place?

Perhaps in terms of right-angled triangles?

Do you mean by using SOHCAHTOA?
 
Since I'm not English, I don't know what SOHCAHTOA means.

I assume it is related to:
[tex]\cos(v)=\frac{adjacentside}{hypotenuse},\sin(v)=\frac{oppositeside}{hypotenuse}[/tex]

Now, what interpretation of sine and cosine do you get if the hypotenuse equals 1?
(Alternatively, you may have learned about how sine and cosine are defined on the unit circle).


In this case, with the hypotenuse equal to 1, what do we get out of the Pythagorean theorem?
 

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