How to rearrange this equation for o

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Homework Help Overview

The discussion revolves around rearranging an equation involving the tangent function, specifically focusing on the variable 'o'. The equation presented includes terms with tan^2(o/2) and is set equal to a variable 't'.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants explore the nature of the functions involved, questioning if both terms are indeed tan^2(o/2). There is a discussion about the associative rule for similar functions. One participant suggests substituting x for tan(o/2) to simplify the equation into a standard quadratic form.

Discussion Status

The discussion is active, with participants raising questions about the functions and exploring different approaches to rearranging the equation. A substitution method has been proposed, leading to a quadratic equation, but there is no consensus on the next steps or solutions.

Contextual Notes

There is some confusion regarding the correct form of the equation, with one participant correcting their earlier post about the terms involved. The original poster expresses frustration about the rearrangement process.

peter456
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o = theta

how the hell do you rearrange for o?

(1/6)tan^2(o/2) + (1/2)tan^2(o/2) = t
 
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Are both functions tan^2(o/2)?

If so, what is the associative rule when functions are the same, i.e. a f(x) + b f(x) ?
 
Last edited:
Astronuc said:
Are both functions tan^2(o/2)?

If so, what is the associative rule when functions are the same, i.e. a f(x) + b f(x) ?
Sorry i made a mistake, it' really:

(1/6)tan^2(o/2) + (1/2)tan(o/2) = t
 
If you let x= tan(o/2) then the equation is (1/6)x2+ (1/2)x= t or, equivalently,
x2+ 3x- 6t= 0. Can you solve that for x (in terms of t)?
 

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