4 1 Radian and Degree Measure I Angles

4. 1 Radian and Degree Measure I. Angles (2 rays: an Initial side & a Terminal side). A) Initial side = the starting ray of the angle. 1) It is on the + x-axis (from the origin). B) Terminal side = the ending ray of the angle. 1) + angles go counter-clockwise. 2) – angles go clockwise. C) This is known as the angle in standard position (initial side starts at the x-axis).

4. 1 Radian and Degree Measure II. Radians and Radian Measure. A) Radian: a way of measuring angles ( symbol θ ). 1) a radian is the ratio of the arc length (s) to the radius (r) of the angle. a) θ = s/r b) it is measured in terms of π. B) One revolution = 360° = 2π radians. C) Finding co-terminal angles (2 angles that end in the same place). 1) Add or subtract 2π from the given angle. D) Complimentary & Supplementary angles: 2 <‘s that add to 1) 90° or π/2 = comp. 2) 180° or π = supple.

4. 1 Radian and Degree Measure III. Special Radian / Degree Angle Measurements. 30° 45° 60° 90° 120° 135° 150° 180° 210° 225° 240° 270° 300° 315° 330° 360°

4. 1 Radian and Degree Measure IV. Converting Degrees to Radians. A) Since 360° = 2π radians, then 180° = π radians. B) Convert using proportions. 1) Degrees to Radians 2) Radians to Degrees x degree x = (degree) π 180° radians π x 180° x = (radians) HW: page 290 # 2 – 52 even