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The Unit Circle, Reference Angles, and Coordinates

The Unit Circle, Reference Angles, and Coordinates. Unit Circle. 1. (0,0). Center: . -1. 1. 1. Radius:. -1. Measure of an Angle. 1. The measure of an angle is determined by the amount of rotation from the initial side to the terminal side. -1. 1. Initial Side. Terminal Side .

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The Unit Circle, Reference Angles, and Coordinates

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  1. The Unit Circle, Reference Angles, and Coordinates

  2. Unit Circle 1 (0,0) Center: -1 1 1 Radius: -1

  3. Measure of an Angle 1 The measure of an angle is determined by the amount of rotation from the initial side to the terminal side. -1 1 Initial Side Terminal Side -1

  4. Coterminal Angles 1 Angles that share the same initial and terminal sides. Example: 30° and 390° -1 1 -1

  5. Reference Angle (R.A.) 0°≤Ө≤90° 90°≤Ө≤180° 1 1 Ө Ө R.A. R.A. -1 -1 1 1 Acute angle formed by the terminal side and the x-axis. R.A. = 180° – Ө R.A. = Ө -1 -1 180°≤Ө≤270° 270°≤Ө≤360° 1 1 Ө -1 1 -1 1 R.A. R.A. Ө R.A. = 360° – Ө R.A. = Ө – 180° -1 -1

  6. 1 (cosӨ,sinӨ) Ө -1 1 -1 Coordinate on Unit Circle Ex: The coordinates for a 210° angle are

  7. Example Reference Angle = 225º - 180º = 45º 225º is in the 3rd quadrant of the unit circle.Another possibility is in the 4th quadrant. Another Possibility: 360º - 45º = 315º

  8. Possibilities: Example - 360º + 360º 30º 390º 750º -330º All Possibilities: 150º 510º 870º -210º + 360º - 360º From the last slide: 180º - 30º = 150º The Graph continues!

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