Amy's Rlection #14

ok this week we started chapter 8. Here's an explanation for 8.1:

1. For any line : m = tan (alpha)
**m = slope , (alpha) = angle of inclination

2. For a conic: tan 2 (alpha) = B/A-C

**if A=C then pie/4 (always)
**A = coefficient of x^2, B = coefficient of xy, C = coefficient of y^2

Examples:

1. Find the angle of inclination of x^2 - 2xy + 3y^2 = 1.

tan 2 (alpha) = B/A-C

A = 1 , B = -2 , C = 3

tan 2 (alpha) = -2/1 -3 = 1

tan 2 (alpha) = 1

2A = tan^-1 (1)

**if the # you're taking the inverse of is positive then find where it's negative and of course if it's negative then find where it's positive

**tan is negative in quad. #1 & 3

2 (alpha) = 45 , 225

alpha = 45/2 , 225/2

alpha = 22.5 , 112.5

2. x^2 + y^2 - 3xy + 4x - sqrt. x = 1

alpha = 1 (because A = 1 & C = 1 so A = C)

Helpful Hints:

quad #1: solve inverse
quad. #2 : make negative and add 180
quad. #3 : just add 180
quad. #4 : make negative and add 360

can someone tell me how you find the x-points and the phase shift. i know you need add something but what..i dont know..someone please help :(