Terms to know going forward Angle: 2 rays an initial side and a terminal side. Initial side Terminal side Positive angle goes counter clockwise. Negative angle goes clockwise. Standard position: vertex of angle at origin Quadrants:III Where is x positive and negative IIIIV Where is y positive and negative Degrees: a rotation from the initial side all the way around to itself ( 1 revolution) is 360 0, 1 0 = 1/360 of a revolution = ¼ of a revolution = ½ of a revolution.

Radians: 1 radian is when the initial ray and terminal ray of an angle are the same length as is the arc of the circle the intersect. This is helpful to understand how to convert from degrees to angle and vice versa. Using this definition and the fact that the circumference of a circle is 2πr if the radius is 1 then the number of radians to make 1 revolution is 2π. Therefore = 2π radians Dividing both side by 2 you find that = π radians Dividing both sides by 180 you find that 1 0 = π/180 radians or Dividing both sides by π you find that /π = 1 radian. We can use these 2 formulas to convert from degrees to radians and vice versa.

Degrees and Radians of a Circle There are in a circle and if the circle has a radius of 1 then there are 2π radians around the circle. Therefore we can measure a circle in degrees or radians. How can you convert degrees to radians? So change to radians

Degrees and Radians of a Circle So change 18 0 to radians You Try So change to radians to radians

Degrees and Radians of a Circle There are in a circle and if the circle has a radius of 1 then there are 2π radians around the circle. Therefore we can measure a circle in degrees or radians. How can you convert radians to degrees? So change π/4 to degrees

Degrees and Radians of a Circle So change 5π/3 to degrees You Try So change 11π/12 to degrees -π/2 to degrees

90 0 or or or or What does some of this look like on a circle. Degrees

π/2 or -3π/2 0 Or 2π 3π/2 or -π/2 π or -π What does some of this look like on a circle. Radians