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Understanding Trigonometric Angles and the Unit Circle

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This introductory unit on trigonometry covers essential concepts such as angle measures, the unit circle, and evaluating trigonometric functions. Starting with the definition of angles formed by rotating rays from a central point, learners will explore standard position angles, complete revolutions, and coterminal angles. The course will include practical examples and problem-solving sessions to ensure comprehension. Key topics include identifying angle measures in various quadrants and applying these concepts within the unit circle framework to evaluate trigonometric functions and arc lengths.

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Understanding Trigonometric Angles and the Unit Circle

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  1. Unit 1: Introduction to Trigonometry LG 1-1: Angle Measures (Test 8/15) LG 1-2: THE Unit Circle (Test 8/21) LG 1-3: Evaluating Trig Functions (Test 8/23) LG 1-4: Arc Length (Test 8/28)

  2. Consider a circle, centered at the origin with 2 rays extending from the center. One ray is fixed along the positive x-axis The other can rotate about the center • These rays form an angle. The fixed ray is called the initial side of the angle. • The other side is called the terminal side. • Any angle with vertex at the origin and initial side along the positive x-axis is in standard position.

  3. As the terminal side is rotated counterclockwise, the measure of the angle that is formed increases. 30o 135o 210o

  4. The rotation of the terminal side may include 1 or more complete revolutions about the center. The measurement representing 1 complete revolution is 360o 1 revolution 360o 2 revolutions 720o 1 revolution + 60o 420o

  5. Angles that differ by one or more complete revolutions are called coterminal angles. • For example: 74o, 434o, and 794o are all coterminal angles. Why? • Think of at least 2 coterminal angles for 105o

  6. The terminal side of an angle can also rotate clockwise. A negative number is used to denote these angle measures. -45o -150o -420o

  7. Suppose these angles are in standard position. Place each angle in the quadrant that contains its terminal side.

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