How to rearrange this equation for o

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In summary, The conversation involves two functions, tan^2(o/2) and tan(o/2), and the associative rule for when functions are the same. The main question is how to rearrange for o in the equation (1/6)tan^2(o/2) + (1/2)tan^2(o/2) = t. A mistake was made in the equation and it should be (1/6)tan^2(o/2) + (1/2)tan(o/2) = t. The person suggests letting x = tan(o/2) and solving the resulting equation x^2 + 3x - 6t = 0 for x in terms of t.
  • #1
peter456
14
0
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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  • #2
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:
  • #3
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
 
  • #4
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)?
 

What is the first step in rearranging an equation for o?

The first step in rearranging an equation for o is to isolate the variable o on one side of the equation by moving all other terms to the other side using inverse operations.

Can I change the order of terms when rearranging an equation for o?

Yes, you can change the order of terms as long as you use the correct inverse operations to maintain the equality of the equation.

What if there are multiple o's in the equation?

If there are multiple o's in the equation, you can combine them into one term before rearranging or use distribution to isolate o on one side of the equation.

Do I need to simplify the equation before rearranging for o?

It is helpful to simplify the equation before rearranging for o, as it can make the process easier. However, it is not always necessary.

Can I rearrange an equation for o if it contains fractions?

Yes, you can rearrange an equation with fractions for o by multiplying both sides of the equation by the least common denominator (LCD) to eliminate the fractions.

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