 Think back to geometry and write down everything you remember about angles.

 Mr. Szwast has meetings after school on the following days, and therefore will not be available:  Wednesday, February 3  Monday, February 8

Section 4.1 NO CALCULATORS!

 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 A Θ B C Terminal Side Initial Side Vertex

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. x y Terminal Side Initial Side Vertex   is positive Positive angles rotate counterclockwise. x y Terminal Side Initial Side Vertex   is negative Negative angles rotate clockwise.

 The rectangular coordinate plane is divided into four quadrants

DegreesRadians  Defined as 1/360 th 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

 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)  Acute angle 0º <  < 90º 90º Right angle 1/4 rotation  Obtuse angle 90º <  < 180º 180º Straight angle 1/2 rotation

 Convert to radians  Draw each angle in standard position.  Identify in which quadrant the angle lies.

 Convert the following angles to radians

 Convert to radians  Draw each angle in standard position.  Identify in which quadrant the angle lies.

 Convert to degrees  Draw each angle in standard position.  Identify in which quadrant the angle lies.

 Convert to degrees  Draw each angle in standard position.  Identify in which quadrant the angle lies.

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

 Find a positive angle less than 360˚ or 2 π that is coterminal with:

 Read Section 4.1  Page 434 #1-73 odd

 Convert the following angles to radians

 Complete the table DegreesRadians 300º -120º

 Find a positive angle less than 360˚ or 2 π that is coterminal with:

 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

 If possible, find the complement and supplement of each angle

AngleComplementSupplement a) b) c) d)

 Find the radian measure of the central angle of a circle of radius 6 yards that intercepts an arc of length 8 yards.

 Find the arc length of a circle of radius 8 feet intercepted by a central angle of 225°.

 Read Section 4.1  Page 434 #1-73 odd  Read Section 4.2

 You have the remainder of class today for the Making Waves Activity.