WildTrig12: Cartesian coordinates and geometry

ok..I love it..

what the shit do we actually use this for in daily life...

It's used for geo statistical analysis to warn you of soil toxicity, population density, traffic congestion, etc. It's used in resolving heat transfer problems. Game programming. Movie effects. Keeping planes from slamming into each other. It occurs grinding food waste and carrying water out of your home. Check out Spira Mirabilis. Trig is everywhere in your daily life.

Dumb Question: Great explanations! But I didn't quite follow how you go from a vector of (1,-3) to the equation 3x+y=?

On the next line you explain the formula

vector=(alpha,beta):-betaX+alp haY=?

However, if I redefine the vector as (-1,3), which is still the same line, I now get -3x-y=-7

Are these equivalent equations? Its been a long time since I've used anything but +,-,*,/ and I'm trying to wrap my head around this again :) Thanks.

Hi. The direction vector doesn't completely determine the line. So if you used (-1,3) as the vector, which is fine, you would get an equation for the line: -3x-y=c for some constant c. To determine c, plug in a point you know on the line.

For example the line 3x+y=4 is the same as the line -3x-y=-4. Hope this helps