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© The Visual Classroom x y 5.2 Understanding Angles terminal arm initial arm standard position initial arm 0 º terminal arm x y non-standard position.

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Presentation on theme: "© The Visual Classroom x y 5.2 Understanding Angles terminal arm initial arm standard position initial arm 0 º terminal arm x y non-standard position."— Presentation transcript:

1 © The Visual Classroom x y 5.2 Understanding Angles terminal arm initial arm standard position initial arm 0 º terminal arm x y non-standard position

2 © The Visual Classroom x y Positive angles rotate counterclockwise ex: 80º x y Negative angles rotate clockwise ex: –120º

3 © The Visual Classroom x y Quadrants I II III IV 0º 90º 180º 270º quadrantangle I II III IV 0º < < 90º 90º < < 180º 180º < < 270º 270º < < 360º

4 © The Visual Classroom x y Example: Let P(x, y) be a point on the terminal arm of an angle in standard position. P(x, y) Point P can be anywhere in the x-y plane. 1 1 is in quadrant II. x y P(x, y) 2 is in quadrant IV. 2 90º < < 180º 270º < < 360º

5 © The Visual Classroom x y 3 P(x, y) 3 lies in the negative x-axis. 3 = 180º

6 © The Visual Classroom Coterminal angles x y They share the same initial arm and the same terminal arm. Ex: 1 = 210º = – 150º

7 © The Visual Classroom x y Coterminal angles share the same initial arm and the same terminal arm. Ex: 1 = 30º = 360º + 30º = 390º 3 = 720º + 30º = 750º 3 x y 4 = – 360º + 30º = – 330º 4

8 © The Visual Classroom The principal angle is the angle between 0º and 360º. The coterminal angles of 390º, 750º and – 330º all share the same principal angle of 30º. The related acute angle is the angle formed by the terminal arm of an angle in standard position and the x-axis. x y 1 The related acute angle lies between 0º and 90º.

9 © The Visual Classroom x y x y x y = 150º = 180º – 150º = 30º = 220º = 220º – 180º = 40º = 325º = 360º – 325º = 35º

10 © The Visual Classroom Example 1: x y – 160º a) –160º will be in quadrant III. principal angle b) The principal angle: b) determine the principal angle. c) determine the related acute angle. a) Sketch an angle of –160º 360º– 160º = 200º c) The related acute angle: 200º– 180º = 20º related acute angle

11 © The Visual Classroom Example 2: 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. c) Determine the principal angle. x y P(–5, –4) 5 4 = 180º + 39º = 219º

12 © The Visual Classroom Example 3: The point P(– 6, 7) lies on the terminal arm an angle in standard position. a) Sketch the angle. b) Determine the value of the related acute angle. c) Determine the principal angle. x y P(–6, 7) 7 6 = 180º – 49.4º = 130.6º

13 © The Visual Classroom Example 4: State all values of, where n I. = 25º + 360ºn, 1 n 3 = 25º + 360º(1) = 385 º = 25 º º (2) = 745 º = 25 º º = 25 º º (3) = 1105 º = 25 º º Answer: {385º, 745º, 1105º }


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