Understanding Angles and Measures in Trigonometry

Delve into the world of angles and their measures in trigonometry, exploring the concepts of degrees and radians. Learn how to convert between degrees, minutes, and seconds, and grasp the relationship between degrees and radians in circular arcs. Discover the fundamentals of radian measure and its significance in calculus and trigonometry.

• Trigonometry
• Angles
• Degrees
• Radians
• Circular Arcs

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1. Pre-AP Pre-Calculus Chapter 4, Section 1 Angles and Their Measures 2013 - 2014

2. Chapter 4 Welcome to Trigonometry!! Pay attention to the difference between degrees and radians. Primarily in this course and Calculus you will use radians.

3. Definition: Radian A central angle of a circle has measure 1 radian if it intercepts an arc with the same length as the radius

4. Degrees and Radians A degree is a unit of angular measure equal to 1/180thof a straight angle. In DMS (degree-minute-second) system, each degree is subdivided into 60 minutes (denoted by ) and each minute is subdivided into 60 seconds (denoted by ).

5. Working with DMS Measure Convert 42 24 36 to degrees

6. Working with DMS Measure Convert 37.425 to DMS

7. Degree - Radian A straight angle (line) has __________ and a radian measure of _________.

9. Working with Radian measures How many radians are in 90 degrees?

10. Working with Radian measures How many degrees are there in ? 3radians?

11. Working with Radian measures How many degrees are in 2? 3radians?

12. Circular Arc Length

13. Arc Length Formula (Radian measure) If is a central angle in a circle of radius r, and if is measured in radians, then the length s of the intercepted arc is given by ? = ??

14. Arc Length Formula (degree measure) If is a central angle in a circle of radius r, and if is measured in degrees, then the length s of the intercepted arc is given by ? =??? 180

15. Perimeter of a Pizza Slice Find the perimeter of a 60 slice of a large (7 inch radius) pizza.

16. Designing a Running Track The running lanes at the Emery Sears track at Bluffton College are 1 meter wide. The inside radius of the lane 1 is 33 meters and inside radius of lane 2 is 34 meters. How much longer is lane 2 than lane 1 around one turn?

17. Angular and Linear Motion Sometimes it is necessary to connect angular speed (measured in units like revolutions per minute) and linear speed (measured in units like miles per hour. The connection is usually given by one of the arc length formulas or by a conversion.

18. Using Angular speed Albert s truck has wheels 36 inches in diameter. If the wheels are rotating at 630 rpm (revolutions per mintue), find the truck s speed in miles per hour.

19. Ch 4.1 Homework Pg. 356 357, # s: 2 24 even, 25, 30, 31, 36, 41, 45 59, 61 20 total problems Gray book: pg. 325