# Tan 50

1. Aug 21, 2004

### benzun_1999

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

2. Aug 21, 2004

### arildno

What's 50?

3. Aug 21, 2004

### 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)

4. Aug 24, 2004

### benzun_1999

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

5. Aug 24, 2004

### chronon

Last edited by a moderator: Apr 21, 2017