Tan 50

[benzun_1999]

Hi
can anyone tell me what is tan 50 in fractions?
-benzun

[arildno]

What's 50?
Radians or degrees?

[arildno]

I'll assume that "50" is in degrees:
What you need is basically an expression for \cos(20) , all the rest follow from this:

1. \cos(60)=\cos(3*20)=4\cos^{3}20-3\cos(20)
by simple trigonometric identities.
Hence, setting y=\cos(20) you find the required value by solving for y in the equation:
4y^{3}-3y=\frac{1}{2} since \cos(60)=\frac{1}{2}
You need therefore the formula for roots of 3.degree polynomials.

2. \cos(10)=\frac{1+y}{2} by the half-angle formula.

3. \cos(50)=\cos(60)\cos(10)+\sin(60)\sqrt{1-\cos^{2}(10)}
by the summation formula for cosine.

4. By noting \sin(50)=\sqrt{1-\cos^{2}(50)} you may find your expression for tan(50)

[benzun_1999]

sorry,
i ment degrees only
Thanks
Is it possible to construct 50 degrees with a compas and scale only?
-benzun

[chronon]

Is it possible to construct 50 degrees with a compas and scale only?
-benzun

See
http://planetmath.org/encyclopedia/ConstructibleAnglesWithIntegerValuesInDegrees.html