Terms to know going forward Angle: 2 rays an initial side and a terminal side. Terminal side Initial side Positive angle goes counter clockwise. Negative angle goes clockwise. Standard position: vertex of angle at origin Quadrants: II I Where is x positive and negative III IV Where is y positive and negative Degrees: a rotation from the initial side all the way around to itself ( 1 revolution) is 3600 , 10 = 1/360 of a revolution. 900 = ¼ of a revolution 1800 = 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 can be found by setting rø = 2πr (circumference) solve for ø and you get ø = 2π or one revoulution is equal to 2π Therefore 3600 = 2π radians Dividing both side by 2 you find that 1800 = π radians Dividing both sides by 180 you find that 10 = π/180 radians or Dividing both sides by π you find that 1800/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 3600 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 1000 to radians

Degrees and Radians of a Circle So change 180 to radians You Try So change 3150 to radians -360 to radians

Degrees and Radians of a Circle There are 3600 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

900 or -2700 00 or 3600 2700 -900 1800 -1800 What does some of this look like on a circle. Degrees

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

Formulas: must use radians Arc of a sector Area of a sector s = rø A = ½ r2 ø If the radius is 3 and the angle is 450 find the arc and area. 450 = π/4 s = 3(π/4) = 2.356 A = ½ (3)2(π/4) =3.534