Simple Trig Equations

Chapter 8-1 is pretty much the same as Chapter 7-6, with a few more added notes.

m=tan(theta), where m is the slope of a line.
theta- "alpha" also known as "angle of inclination."

tan2(theta)= B/A-C finds the "angle of inclination" of a conic.
Ax^2+Bxy+Cy^2+...=___

Example 1:
Solve:
3cos(theta)=1
*divide both sides by 3
theta=cos^-1=1/3
*which gives you 70.529
*cosine is positive in the first and fourth quadrants
*make 70.529 negative and add 360 to move it to the fourth quadrant
-70.529+360=289.471degrees
*you must change to degrees, minutes, and seconds
=70degrees31'44'' and 289degrees28'15''

Example 2:
Solve:
6csc(theta)-9=0
*First, add nine to 0.
*divide by 6 on both sides
theta=csc^-1(3/2)
*which would be sin^-1(2/3)
=41.810
*sin is positive in the first and second quadrants
*make 41.810 negative and add 180 to move it to the second quadrant
-41.810+180=138.19degrees
*you have to change both to degrees, minutes, and seconds
=41degrees48'36'' and 138degrees11'24''

Example 3:
Solve:
5sec(theta)+6=0
*subtract 6 from 0
*divide both sides by 5
theta=sec^-1-(6/5)
*which would be cos^-1(-5/6)
=33.557degrees
*cosine is negative in the second and third quadrants
*make 33.557 negative and add 180 to move it to the second quadrant and add 180 to 33.557 to move it to the third quadrant
=176.443degrees and 213.557degrees
*youhave to change both to degrees, minutes, and seconds
=176degrees26'34'' and 213degrees33'25''