# Calculating the length of a tangent curve

1. May 17, 2012

### keeaga

Considering f(x) = tan(x) * 5 / 8 ......

how can I find the length of the curve, specifically, between (0, 0) and (1, 1) ?

if anyone can help I would be happy.

Thanks
Keeaga

2. May 17, 2012

### DonAntonio

You can't: the point (1,1) is not on the function's graph.

DonAntonio

3. May 18, 2012

### keeaga

Actually, it is... that's what the 5/8 is for. It shrinks the tangent vertically just enough for the curve to cross (-1,-1), (1,1), and (0,0).

I still don't know how to go about finding the length of the curve though.

Keeaga

4. May 18, 2012

### Mandlebra

Are you implying tan(1)*5/8= 1?

5. May 18, 2012

### DonAntonio

No, it really doesn't: $\,\tan 1=1.55741\Longrightarrow \frac{5}{8}\tan 1 = 0.97338\neq 1\Longrightarrow (1,1)\,$ is not on the graph of the function, and neither

is the point $\,(-1,-1)\,$

DonAntonio

6. May 20, 2012

### keeaga

Ok, sorry, you're right... Thought it crossed 1,1 but that was based on a graph of it only.

Still, anyone know how generally to find the length of a tangent curve?

KTM

7. May 20, 2012

### Vargo

Check out the wikipedia entry on arclength where there are many formulas. Also, any calculus text will have arclength formulas. The key to them all is the Pythagorean theorem

ds = sqrt(dx^2+dy^2). Divide out dx and you get sqrt(1+(dy/dx)^2) dx