Day 1: Angles In Standard Position

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

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

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

4. y y x x 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 270º < q2 < 360º q2 q2 is in quadrant IV. P(x, y)

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

6. y x The principal angle is the angle between 0º and 360º. 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. y y y x x x q q b b q = 220º b = 220º – 180º q = 150º = 40º b = 180º – 150º = 30º q = 325º b b = 360º – 325º q = 35º

8. y x Example 1: The point P(–5, –4) lies on the terminal arm an angle in standard position. 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. y x Example 2: The point P(– 6, 7) lies on the terminal arm an angle in standard position. 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