Trigonometry (Double angle formula)

[trollcast]

Homework Statement

Calculate the value of \tan(\frac{\pi}{12}) without the use of a calculator and showing all steps.

Homework Equations

Compound angle formula / Double angle formula

The Attempt at a Solution

Using an equilateral triangle of side length 2 I've shown that:
$$\tan(\frac{\pi}{6})=\frac{1}{\sqrt{3}}$$
Then using the double angle formula:
$$\tan(2\theta)=\frac{2\tan(\theta)}{1-\tan^2(\theta)}$$
Substituting the value for \tan(\frac{\pi}{12}) in as 2θ and solving for \tan(\theta):
$$\tan(\frac{\pi}{12})=\pm2-\sqrt(3)$$

However how do I show that I only need to take the positive solution?

Thanks

 

[micromass]

You know that $\pi/12$ is in the first quadrant. What must the tangent be of an angle in the first quadrant? Positive or negative?

 

[trollcast]

You know that $\pi/12$ is in the first quadrant. What must the tangent be of an angle in the first quadrant? Positive or negative?

Thanks micro don't know how I missed that.

So the tangent should be positive since its in the first quadrant, therefore the negative solution is not possible?

 

[micromass]

That's it!

 

[trollcast]

That's it!

Thanks again, I just actually realized I could have done it by finding \tan(\frac{\pi}{4}) and then using the compound angle formula to calculate \tan(\frac{\pi}{4}-\frac{\pi}{6}) , which would only give one solution at the end.