1. Day 1: Angles In Standard Position
terminal arm q
initial arm
standard position
non-standard position x y x y
terminal arm q q q
initial arm 0º

2. y
Positive angles
ex: 80º
rotate counterclockwise q x x y
Negative angles
rotate clockwise q
ex: –120º

3. Quadrants II I III IV x y quadrant angle I II III IV
90º II I
quadrant
angle I II
III IV
0º < q < 90º
180º
90º < q < 180º 0º
180º < q < 270º
III IV
270º < q < 360º
270º

4. x y
Example:
P(x, y)
Let P(x, y) be a point on the terminal arm of an angle in standard position. q1
Point P can be anywhere in the x-y plane.
q1 is in quadrant II.
90º < q1 < 180º x y
270º < q2 < 360º q2
q2 is in quadrant IV.
P(x, y)

5. x y
q3 = 180º
P(x, y) q3
q3 lies in the negative x-axis.

6. The principal angle is the angle between 0º and 360º.x y
The related acute angle is the angle formed by the terminal arm of an angle in standard position and the x-axis. q1 b
The related acute angle lies between 0º and 90º.

7. x y x y q q b b
q = 220º
b = 220º – 180º
q = 150º
= 40º
b = 180º – 150º x y
= 30º
q = 325º
b = 360º – 325º b q
= 35º

8. b) Determine the value of the related acute angle. q
Example 1: The point P(–5, –4) lies on the terminal arm an angle in standard position. x y
a) Sketch the angle.
b) Determine the value of the related acute angle. q 5 b 4
P(–5, –4)
c) Determine the principal angle q.
q = 180º + 39º
q = 219º

9. b) Determine the value of the related acute angle. q
Example 2: The point P(– 6, 7) lies on the terminal arm an angle in standard position. x y
P(–6, 7)
a) Sketch the angle.
b) Determine the value of the related acute angle. 7 q b 6
c) Determine the principal angle q.
q = 180º – 49.4º
q = 130.6º