8-1

In Advanced Math this week, we learned and reviewed sections of Chapter 8. In 8-1 part II, we learned how to find angle of inclinations and direction angles.

To find the angle of inclination, keep in mind that alpha = angle of inclination.
Also, m=tan alpha for a line.
tan 2alpha = B/A-C – if A is not equaled to C
alpha = pi/4 – if A = C

EXAMPLE 1: To the nearest degree, find the inclination of the line 3x+5y=15
A). First thing you need to do is solve for y. So, you will then get y=3/5x-3.
B). Next, you know that m=tan alpha so look at the problem and the number before x will be your tan alpha. In this problem it is 3/5.
C). Now find the inverse.. alpha = tan^-1(3/5) *(Remember, you have to find the inverse of a positive number).
D). Draw your coordinate plane. Your quadrant 1 angle is 40 degrees. Tangent is positive in quadrant 3, so add 180 degrees to 40 degrees to get 220 degrees.

EXAMPLE 2: Find the direction angle alpha, x^2-2xy+y^2=1.
A). According to the notes above, check your A and C first. They are both 1, so your answer will simply be pi/4.

EXAMPLE 3: Find the direction angle alpha, -6x^2-2xy+4y^2=1.
A). According to the notes above, check you’re a and C first. In this problem they are not equaled so you will continue to work the problem out with the function tan 2alpha = B/A-C.
B). Plug your numbers into the function.. tan 2alpha = -2/-6+4 à tan 2alpha = 1
C). tan 2alpha = 1. Now find the inverse.
D). Draw your coordinate plane and place 45 degrees in quadrant one. Since tangent is positive in quadrant 3, add 180 degrees to 45 degrees to get 225 degrees.
E). Now that we’ve found our two angles, divide them by 2. *(Remember, the 2 didn’t disappear so you must divide your angles by 2 to get alpha =).
F). Your final answer is alpha = 22.5 degrees, 112. 5 degrees

This section is pretty much following functions. If you know your functions then all you have to do is plug in the numbers and solve. Also, it is just repetition of 8-1 part I.