Unraveling the Mystery of Theta: Solving Cot(2theta) = 2

[mattmannmf]

what is Theta?

Cot (2theta) = 2

I have no idea how to get the answer. algebraically or in my calculator

 

[Char. Limit]

Well, you don't have the inverse cottangent button on your calculator, so you might want to turn that cotangent into something that has an inverse button on your calculator... how about tangent?

 

[mattmannmf]

ok:

so cot (2 theta)= 2

can be:
(2 theta) = tan(2)

is that correct?

 

[Char. Limit]

Not quite.

$$cot(\theta)=\frac{1}{tan(\theta)}$$

 

[mattmannmf]

I have no idea than..

 

[Char. Limit]

Try taking the reciprocal of both sides...

I'll do one step for you.

Original equation...

$$cot(2\theta)=2$$

Take the reciprocal...

$$\frac{1}{cot(2\theta)}=\frac{1}{2}$$

And use the identity I told you before...

$$tan(2\theta)=.5$$

And you can solve it from there with a good calculator!