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Understanding Coterminal Angles and the Unit Circle

In this lesson, we will explore coterminal angles by determining positive and negative angles. You'll learn how to convert degrees to radians and vice versa, while also preparing for a quiz on these concepts. Furthermore, we'll delve into the Unit Circle, a crucial mathematical tool centered at the origin with a radius of 1. Understanding reference angles and their measurements, which lie between 0° and 90°, is paramount for solving trigonometric problems. Get ready to memorize key coordinates and apply them throughout the semester!

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Understanding Coterminal Angles and the Unit Circle

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  1. Warm UP! Name the quadrant. 1. 2. 258 Determine a positive and negative coterminal angle 3. 52  4. -36  Convert from Degrees to Radians or vice versa: 5. 90 6.

  2. QUIZ 1-1 After the quiz, we will be working on the UNIT CIRCLE (EXCITING!!!!)

  3. The Unit Circle is a circle centered at the origin on the coordinate plane with radius = 1

  4. Reference angles • the positive acute angles formed between the terminal side of an angle in standard position and the closest side of the horizontal x-axis. • All reference angles measure between 0o and 90o

  5. 45o 120o 275o 195o

  6. Reference AnglesTo find a reference angle in…

  7. Find the reference angle. c.  = -240° b.  = a.  = 300° 120°, -240° 60° 60° 300° 180°-120° 360° - 300° ref. angle = 60° ref. angle = 60°

  8. Practice: Find the reference angles • 300o • 210o • 135o • 585o • 30o • 870o • -100o

  9. The Unit Circle

  10. The Unit Circle 0

  11. Solve for x: SOHCAHTOA (0,1) Solve for y: hyp 1 y opp 45° 90° (1,0) x adj

  12. Memorize these coordinates on the unit circle. We will use them for the rest of the semester!

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