Question

If -798° is in standard position, determine a coterminal angle that is between 0° & 360° and state the quadrant in which the terminal side lies.

Answer 1

Remark
There are two things you need to realize
1. You are traveling around the quadrants in a clockwise direction.
2. You will wind up with a minus angle between 0 and - 360 which will be different than if you were traveling counterclockwise.

Method
step one
divide - 798 by 360
-798 / 360 = - 2.21666667

Step Two
Drop the integer (in this case minus two). You get
-0.2166666667

Note the minus 2 indicates that you have traveled around the circle twice (that explains the 2) in the clockwise direction (that explains the minus). Minus means clock wise.

Step Three
Multiply the fraction amount by 360 to get the actual angle
-0.2166666667 * 360 = - 78 degrees.

Step Four
Discuss the answer.
You should realize two things.
1. You are in the fourth quadrant with - 78 degrees.
2. If you want the positive equivalent, add 360 to your answer.
- 78 + 360 = 282
Answer 
- 78 degrees
262 degrees.

Comment
If you know what the sine Cosine and Tangent is, you can check that these are the same thing with your calculator

    x =              - 798             - 78           282
Sin(x)             -0.9781         -0.9781    -0.9781              
Cos(x)
Tan(x)

If you do not know how to enter this into your calculator make sure you are in degrees and follow this procedure.
sin(
-
798
=
Answer
1. You are in the 4th quadrant.
2, The positive angle is 282 which is between 0 and 360