Objectives: Be able to draw an angle in standard position and find the positive and negative rotations. Be able to convert degrees into radians and radians.

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Presentation transcript:

Objectives: Be able to draw an angle in standard position and find the positive and negative rotations. Be able to convert degrees into radians and radians into degrees. Be able to find complementary and supplementary angles in radians and degrees. Be able to find co-terminal angles in radians and degrees Be able to find the arc length and Area of a sector. Critical Vocabulary: Positive Rotation, Negative Rotation, Standard Position, Quadrantal Angle, Co-terminal, Degrees, Radians

Ray: Starts at a point and extends indefinitely in one direction. B C Angle: Two rays that are drawn with a common vertex B A Positive Rotation: The angle formed from the initial side to the terminal side rotating counter- clockwise. Negative Rotation: The angle formed from the initial side to the terminal side rotating clockwise. Standard Position: The vertex of an angle is located at the origin Terminal Side Initial Side Lies in Quadrant: The location of the terminal side.

 = 315 degrees  = 315 degrees  = -45 degrees Lies in Quadrant 4  (theta) = the angle measurement. Reference Angle: The angle between the terminal ray and the x-axis. 1.  = 360 degrees = 1 revolution 2.  = 90 degrees = ¼ revolution 3.  = 180 degrees = ½ revolution 4.  = 260 degrees = 13/18 revolution Example 1: Draw an angle of 315° in standard position  = 315 degrees Initial Side  = 315 degrees  = -45 degrees Terminal Side Lies in Quadrant 4 Reference: 45 degrees

 = -125 degrees  = 235 degrees  = -125 degrees Lies in Quadrant 3  (theta) = the angle measurement. 1.  = 360 degrees = 1 revolution 2.  = 90 degrees = ¼ revolution 3.  = 180 degrees = ½ revolution 4.  = 260 degrees = 13/18 revolution Example 2: Draw an angle of -125° in standard position  = -125 degrees Initial Side  = 235 degrees  = -125 degrees Terminal Side Lies in Quadrant 3 Reference: 55 degrees

 = 460 degrees  = 100 degrees  = -260 degrees Lies in Quadrant 2  (theta) = the angle measurement. 1.  = 360 degrees = 1 revolution 2.  = 90 degrees = ¼ revolution 3.  = 180 degrees = ½ revolution 4.  = 260 degrees = 13/18 revolution Example 3: Draw an angle of 460° in standard position Terminal Side  = 460 degrees  = 100 degrees Initial Side  = -260 degrees Lies in Quadrant 2 Reference: 80 degrees

 = -1020 degrees  = 60 degrees  = -300 degrees Lies in Quadrant 1  (theta) = the angle measurement. 1.  = 360 degrees = 1 revolution 2.  = 90 degrees = ¼ revolution 3.  = 180 degrees = ½ revolution 4.  = 260 degrees = 13/18 revolution Example 4: Draw an angle of -1020° in standard position Terminal Side  = -1020 degrees  = 60 degrees Initial Side  = -300 degrees Lies in Quadrant 1 Reference: 60 degrees

 = -270 degrees  = 90 degrees  = -270 degrees Quadrantal Angle  (theta) = the angle measurement. 1.  = 360 degrees = 1 revolution 2.  = 90 degrees = ¼ revolution 3.  = 180 degrees = ½ revolution 4.  = 260 degrees = 13/18 revolution Example 5: Draw an angle of -270° in standard position Terminal Side  = -270 degrees  = 90 degrees Initial Side  = -270 degrees Quadrantal Angle Quadrantal Angle: Terminal side is located on an axis

Page 862-863 #3-9 all, 14 Directions (#3-9): 1. Draw the Angle in Standard Position 2. How many complete rotations 3. What are Alpha and Beta 4. What Quadrant does the Angle Lie in 5. What is the Reference Angle

Page 862 -863 #3, 4, 6-9 all, 14 Rotations: 0 Alpha: 120 degrees Beta: -240 degrees Lies in Quadrant II Reference Angle: 60 degrees 9. Rotations: 2 Alpha: 180 degrees Beta: -180 degrees Quadrantal Angle Reference Angle: None 4. Rotations: 1 Alpha: 240 degrees Beta: -120 degrees Lies in Quadrant III Reference Angle: 60 degrees 14. C 6. Rotations: 0 Alpha: 110 degrees Beta: -250 degrees Lies in Quadrant II Reference Angle: 70 degrees 7. Rotations: 0 Alpha: 350 degrees Beta: -10 degrees Lies in Quadrant IV Reference Angle: 10 degrees 8. Rotations: 1 Alpha: 90 degrees Beta: -270 degrees Quadrantal Angle Reference Angle: None