Warm-Up: January 8, 2014

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.