1. Ch 4 Trigonometric Functions
4.1 Radian and Degree Measure

2. Trigonometry (from Greek) the measurement of triangles
Originally used in the development of astronomy, navigation and surveying
After development of calculus and physical science in 17th century, used for rotations and vibrations, sound waves, light rays, planetary orbits, vibrating strings, pendulums, and orbits of atomic particles.

3. Angles Determined by rotating a ray around it’s end

4. Positive and Negative Angles

5. Coterminal Angles

6. Radian Measure Definition of Radian:
One radian (rad) is the measure of a central angle that intercepts an arc s in equal length to the radius of the circle.

9. Example: Sketching and Finding Coterminal Angles

10. Example: Sketching and Finding Coterminal Angles

11. Example: Sketching and Finding Coterminal Angles

12. Complementary and Supplementary Angles

13. Degree Measure

14. Conversion

15. Practice: Convert to degrees

16. Practice: Convert to radians

17. Arc Length
A circle has a radius of 27 inches. Find the length of the arc intercepted by a central angle of 160o

18. Linear and Angular Speed (Constant speed along a circular path.)
Consider a particle moving at a constant speed along a circular arc of radius r. If s is the length of the arc traveled in time t, the linear speed of the particle is
If is the angle (in radian measure) corresponding to the arc length s, then the angular speed of the particle is

19. Example:
The second hand of a clock is 8 cm long. Find the linear speed of the tip of this second hand as it passes around the clock face.

20. Example:
The circular blade on a saw rotates at 2400 revolutions per minute.
Find the angular speed in radians per second.
The blade has a radius of 4 inches. Find the linear speed of a blade tip in inches per second.