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Warm-Up: January 8, 2014

Warm-Up: January 8, 2014. Think back to geometry and write down everything you remember about angles. Angles and Their Measure. Section 4.1 NO CALCULATORS!. C. A. Θ. Terminal Side. Initial Side. B. Vertex. Definitions.

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Warm-Up: January 8, 2014

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  1. Warm-Up: January 8, 2014 • Think back to geometry and write down everything you remember about angles.

  2. Angles and Their Measure Section 4.1 NO CALCULATORS!

  3. C A Θ Terminal Side Initial Side B Vertex Definitions • A ray is a part of line that has one endpoint and extends forever in one direction (arrow) • An angle is formed by two rays that have a common endpoint, called the vertex • The initial side of an angle is where it starts • The terminal side of an angle is where it ends

  4. y y is positive Terminal Side  Vertex Initial Side x x Vertex  Terminal Side Initial Side is negative Positive angles rotate counterclockwise. Negative angles rotate clockwise. Angles of the Rectangular Coordinate System • An angle is in standard position if • its vertex is at the origin of a rectangular coordinate system and • its initial side lies along the positive x-axis.

  5. Quadrants • The rectangular coordinate plane is divided into four quadrants

  6. Defined as 1/360th of a full rotation • 360˚ in a circle • Converted to radians by multiplying by • Defined as the measure of the central angle of a circle that intercepts an arc equal in length to the radius of the circle • 2π radians in a circle • Converted to degrees by multiplying by Degrees Radians

  7. 180º  90º  Acute angle 0º <  < 90º Right angle 1/4 rotation Obtuse angle 90º <  < 180º Straight angle 1/2 rotation Special Angle Names • An acute angle measures less than 90˚ (π/2 radians) • A right angle measures exactly 90˚ (π/2 radians) • Often indicated by a small square at the vertex • An obtuse angle measures between 90˚ and 180˚ (π/2 and π radians) • A straight angle measures exactly 180˚ (π radians)

  8. Example 1 • Convert to radians • Draw each angle in standard position. • Identify in which quadrant the angle lies.

  9. Warm-Up: January 10, 2014You-Try #1 • Convert to radians • Draw each angle in standard position. • Identify in which quadrant the angle lies.

  10. Example 1 ½ • Convert to degrees • Draw each angle in standard position. • Identify in which quadrant the angle lies.

  11. You-Try #1 ½ • Convert to degrees • Draw each angle in standard position. • Identify in which quadrant the angle lies.

  12. Assignment • Page 434 #1-17 odd, 37-51 odd

  13. Coterminal Angles • Coterminal angles have the same initial and terminal sides. • Coterminal angles differ by a multiple of 360˚ or 2π • An angle of x is coterminal with angles where k is an integer

  14. Example 2 • Find a positive angle less than 360˚ or 2πthat is coterminal with:

  15. You-Try #2 • Find a positive angle less than 360˚ or 2πthat is coterminal with:

  16. Complements and Supplements • Two positive angles are complements if their sum is 90˚ (π/2) • Complement of x˚ = 90˚- x˚ • Complement of x = π/2 – x • Two positive angles are supplements if their sum is 180˚ (π) • Supplement of x˚ = 180˚- x˚ • Supplement of x = π – x

  17. Example 3 • If possible, find the complement and supplement of each angle

  18. You-Try #3 • If possible, find the complement and supplement of each angle

  19. Assignment • Page 434 #19-30 ALL

  20. Making Waves Activity • You have the remainder of class today and all of class tomorrow for the Making Waves Activity.

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