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Parts of an Angle

Parts of an Angle. alpha – common angle name. (the rotating side). (the fixed side). Each angle above is said to be in the “standard position” – the vertex is at the origin and the initial side is on the positive x-axis. Example 1. (FYI: The ‘ is read as minutes; the “ is read as seconds).

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Parts of an Angle

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  1. Parts of an Angle alpha – common angle name (the rotating side) (the fixed side) Each angle above is said to be in the “standard position” – the vertex is at the origin and the initial side is on the positive x-axis.

  2. Example 1 (FYI: The ‘ is read as minutes; the “ is read as seconds)

  3. An angle in the standard position in which the terminal side coincides with one of the axes. Quadrantal Angle Examples: Example 2 (Past 360°)

  4. Two angles in standard position that have the same terminal side. All angles have an infinite number of coterminal angles. Coterminal angles are in the form of: where k is some integer. Coterminal Angles 45º 405º (1 loop) 765º (2 loops) Example 3 Begin with the generic form to identify all coterminal angles: a. 45° b. 225° Choose a positive integer for k to find one positive angle: 225 + 360(2) = 945° 45 + 360(1) = 405° Choose a negative integer for k to find one negative angle: 45 + 360(-1) = -135° 45 + 360(-2) = -675°

  5. Implies that the coterminal angle should be positive. In other words, we need to find the value of alpha in Example 4 a. 775° Find the number of rotations (k) by dividing the degree by 360: k = 2 k = -3 Determine the leftover degrees: Method 1 Method 2: (Partial rotation) b. -1297° To convert to a positive angle: Which quadrant does the terminal side of each lie in? Quadrant 2

  6. 120° -135° Example 5 Reference angle: an acute angle formed by the terminal side of a given angle and the x-axis. a. 120° Convert to a positive angle: 360 – 135 = 225 b. -135° Visualize it: 225° Since it’s in Quadrant II: Since it’s in Quadrant III:

  7. HW: Page 280

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