Trigonometry - compound angels

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Homework Help Overview

The discussion revolves around evaluating a trigonometric expression involving the tangent of two angles, specifically tan(37) and tan(23), without the use of calculators or tables. The problem is situated within the context of trigonometry, focusing on identities and relationships between angles.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the possibility of using trigonometric identities, particularly the tangent of a sum identity. Some express uncertainty about how to approach the evaluation of tan(37) and tan(23), while others suggest breaking down tangent into sine and cosine components.

Discussion Status

The discussion is ongoing, with participants exploring different approaches to the problem. Some guidance has been offered regarding the use of identities, but there is no explicit consensus on a single method to solve the problem.

Contextual Notes

There is a playful remark about the terminology used in the thread title, indicating a potential misunderstanding of the terms "angels" and "angles." This may reflect the informal nature of the discussion.

Michael_Light
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Homework Statement



Evaluate http://img828.imageshack.us/img828/3383/msp588119g042f0f3ba0368.gif without using calculator or tables.

Homework Equations





The Attempt at a Solution



I have no ideas how tan37 and tan23 can be found... can anyone give me some hints? The answer given is √3. Thank you...
 
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I don't think you're meant to evaluate tan 37 and tan 23 directly, but do you know any identities which may be used? Like any sum of sin or cos rules? Hint: break tan down into it's sin and cos parts.

(37+23 = 60, and I'd wager you know the sin cos and tan of 60)
 
Actually, I don't think you need to express tangent in terms of sine and cosine. Just use the tangent of a sum identity.

Given
[tex]\tan (a + b) = \frac{\tan a + \tan b}{1 - \tan a \tan b}[/tex]

solve for "tan a + tan b".
 
Compound "angels" huh?

You know, of course, that there's a difference between an angel and an angle?:wink:
 

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