Download - Objectives:
Objectives:1. Be able to draw an angle in standard position and find the
positive and negative rotations. 2. Be able to convert degrees into radians and radians into
degrees. 3. Be able to find complementary and supplementary angles
in radians and degrees.4. Be able to find co-terminal angles in radians and degrees5. 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.
Angle: Two rays that are drawn with a common vertex
Positive Rotation: The angle formed from the initial side to the terminal side rotating ___________________. Negative Rotation: The angle formed from the initial side to the terminal side rotating __________________.Standard Position: ___________________________________.
Lies in Quadrant: ____________________________________.
1. = 360 degrees = __________
2. = 90 degrees = ___________
3. = 180 degrees = ___________
Example 1: Draw an angle of _______° in standard position
(theta) = the angle measurement.
= ________________
= ________________
= ________________
4. = 260 degrees = ___________
Lies in Quadrant ______
Reference: __________
Reference Angle: _________________________________________________________________________________________________________
Example 2: Draw an angle of _______° in standard position
= ________________
= ________________
= ________________
Lies in Quadrant ______
Reference: __________
Example 3: Draw an angle of _______° in standard position
= ________________
= ________________
= ________________
Lies in Quadrant ______
Reference: __________
Example 4: Draw an angle of _______° in standard position
= ________________
= ________________
= ________________
Lies in Quadrant ______
Reference: __________
Example 5: Draw an angle of _______° in standard position
= ________________
= ________________
= ________________
Lies in Quadrant ______
Reference: __________
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
Converting Degrees and radians 1 ______________revolution
180 _____________________ 1 _______________________
Example 6: Convert _____ degrees into radians
Example 7: Convert _______radians into degrees
Complementary Angles: 2 angles sum is 90 degrees __________________ Supplementary Angles: 2 angles sum is 180 degrees _________________ Co-Terminal Angles: Angles in Standard position with terminal sides that coincide Example 8: Give two angles in degrees that are
Complementary
Example 9: Give two angles in degrees that are Supplementary
Example 10: Give two angles in degrees that are Coterminal
Example 11: Give two angles in radians that are Complementary
Example 12: Give two angles in radians that are Supplementary
Example 13: Give two angles in radians that are Coterminal
Example 14: Determine two co-terminal angles (one positive and one negative) for the angle 7π/6.
Example 15: Find the complement and supplement of the angle π/12
Read: Page 861-862Page 863 #15-37 odds
Example 16: Draw an angle of _______° in standard position
= ________________
= ________________
= ________________
Lies in Quadrant ______
Reference: __________
Example 17: Draw an angle of _______° in standard position
= ________________
= ________________
= ________________
Lies in Quadrant ______
Reference: __________
Example 18: Draw an angle of _______° in standard position
= ________________
= ________________
= ________________
Lies in Quadrant ______
Reference: __________
Worksheet: “Drawing Angles in Standard Position”
1. 318
442.
9
793.
90
4. 227
405.
9
326.
5
7. 245
8. 1388