estimate angle between two lines y = 1000x and y = 999x

Question

How to estimate the angle between line y = 1000 x and y = 999 x?

I use the calculator and get 10^(-6) but how to approximate it by hand. Does it relate to Taylor Expansion?

You should probably post this over at [Mathematics Stack Exchange](http://math.stackexchange.com). — Zev Eisenberg, Oct 20 '14 at 23:50
This question appears to be off-topic because it is not a problem specific to programming. — Felix Kling, Oct 20 '14 at 23:52

score 0 · Answer 1 · edited Apr 13 '17 at 12:19

The slope of the first line is 1000 and that of the second is 999. Simply use the formula

\theta = \arctan\frac{m_1-m_2}{1+m_1m_2},

where m_1 is the slope of 1000 and m_2 is the slope of 999.

You should get an answer of 1.00099×10^{-6} radians.

To use a Taylor-McLaurin series, you should go by https://math.stackexchange.com/questions/348711/maclaurin-series-for-arctanx-by-successive-differentiation, and substitute the value of \frac{m_1-m_2}{1+m_1m_2} for x in each of the successive terms.

1 Answers1