1. Angles – An angle is determined by rotating a ray about its endpoint. Vertex Initial Side Terminal Side Terminal Side – Where the rotation of the angle ends Initial Side – Where the rotation of the angle begins Standard Position: 1) Vertex at the origin 2) Initial side coincides with the positive x-axis Positive RotationNegative Rotation

2. Degrees 0°, 360° 90° 180° 270° Degrees can be represented by: Degrees ° Minutes ‘ Seconds “ 1° = 60’ 1’ = 60” 1° = 3600” One full counterclockwise rotation is 360°. To go from Degree/Minutes/Seconds to Decimal 20° 25’ 30” = 20 + 25/60 + 30/3600= 20.425 On calculator use 2 nd apps to pull up the degree and minute symbols. Use alpha + for the seconds symbol. To go from Decimal to Degree/Minutes/Seconds 20.425 = Type in 20.425 then hit 2 nd Apps 4:DMS = 20° 25’ 30”

3. Radians 0, 2π ≈ 6.28 π/2 ≈ 1.57 π ≈ 3.14 3π/2 ≈ 4.71 One radian is the measure of a central angle θ that intercepts an arc s equal in length to the radius r of the circle. One full counterclockwise rotation is 2π Finding an Arc Length (s) Given: Radius = 4 and Central Angle = 4π/3 s = r θ s = 4 (4π/3) s = 16π/3 s = 16.76

4. Degrees and Radians 1° = π /180 1 radian = 180°/π Try these: convert degrees to radians 1. 135° = 2. 540° = 3. -270° = 135 deg (π rad / 180 deg) = 3π / 4 rad 540 deg (π rad / 180 deg) = 3π rad -270 deg (π rad / 180 deg) = -3π / 2 rad Try these: convert radians to degrees 1. -π/2 rad = 2. 9π/2 rad = 3. 2 rad = -π/2 rad (180 deg / π rad) = -90° 9π/2 rad ( 180 deg / π rad) = 810° 2 rad ( 180 deg / π rad) = 114.59°

5. Complementary & Supplementary Two positive angles are complementary if their sum is 90° or π/2 radians. Two positive angles are supplementary if their sum is 180° or π radians Try these: find the complement 1. 40° = 2. 2π/5 = 3. 3π/4 = 90° – 40° = 50° π/2 – 2π/5 = π/10 π/2 – 3π/4 = -π/4 *so angle is too big to have a complement Try these: find the supplement 1. 120° = 2. 2π/5 = 3. 3π/4 = 180° – 120° = 60° π – 2π/5 = 3π/5 π – 3π/4 = π/4