Understanding Radian and Degree Measure in Trigonometry

1. Chapter 4 Section 1 Radian and Degree Measure

2. Trigonometry • Greek meaning “measurement of triangles” (surveying, navigating) • Expanded into rotation and vibrations (calculus, physical sciences, (sound waves, light rays))

3. Standard position – initial side on the positive x-axis Counterclockwise – positive angle Clockwise – negative angle Angles Terminal side Initial side vertex

4. Angles that have the same initial side and the same terminal side Coterminalangles Coterminal angles

5. Degree measure 900 1800 O0 = 3600 2700 1° is equivalent to a rotation of 1/360 of a revolution

6. coterminal angles of 600 negative = -3000 positive = 4200

7. D0M’S” 1’ = 1/60(10) 1” = 1/3600(10) Convert Calculator: angle menu Convert degrees, minutes, seconds to decimal

8. From a central angle of a circle, when the length of an arc = the radius of the circle then it is 1 radian measure Radian Measure θ S = arc length If s = r then θ = 1 radian s θ r

9. Arc length = radian * radius • s = θr • If s = full circle then s = circumference • C = 2πr • s = 2πr • rθ = 2πr • θ = 2π radians = 1 revolution = 3600

10. If = 2, then… /2 rad = 900 0 rad = 00 2rad = 3600 rad = 1800 3/2 rad = 2700 1/2θ = ½(2π) = π radians = 1800 1/4θ = ¼(2π) = π/2 radians = 90o 3/4θ = ¾(2π) = 3π/2 radians = 2700

11. Quadrants and common radians /3 /2 /4 I 0<θ</2 II /2<θ< /6 III <θ< 3/2 IV 3/2 <θ< 2 o=2 Quadrants Common radians

12. 1. positive coterminal 2. positive coterminal 3. negative coterminal Examples: Sketch the angle and find a coterminal angle

13. 1. Find the complementary and supplementary angles complementary supplementary Example:

14. converting from degrees to radians converting from radians to degrees Converting degrees and radians

15. Examples 1. convert 1200 to radians 2. convert -3150 to radians

16. convert to degrees convert 7 radians to degrees Example