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

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

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

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)

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

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.

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

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

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