How to rearrange this equation for o

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The discussion focuses on rearranging the equation (1/6)tan^2(o/2) + (1/2)tan(o/2) = t to solve for the variable o. The equation can be simplified by substituting x = tan(o/2), resulting in the quadratic equation x^2 + 3x - 6t = 0. This quadratic can be solved using the quadratic formula, yielding solutions for x in terms of t. The final step involves back-substituting to find o from the value of x.

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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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