7 1 measurement of angles
Download as PPTX, PDF3 likes1,261 views
This document discusses trigonometry and angles. It defines angles in degrees and radians, and coterminal angles. Degrees can be divided into minutes and seconds. One radian is defined as the central angle whose arc length equals the radius. Conversions between degrees and radians are provided. Coterminal angles have the same terminal ray but different measures. Examples are given to find coterminal angles of π/4 and 4π/3.
1 of 15
Downloaded 36 times
7 1 measurement of angles
- 1. Objectives: 1. Measure angles in degrees and radians 2. Find coterminal angles
- 2. Trigonometry comes from Greek words meaning “triangle measurement.” Has been used for centuries in navigation and surveying.
- 3. In trig, angles represent rotations about a point. One revolution (complete rotation) contains 360 . Degrees can be divided into 60 minutes and each minute into 60 seconds. Example: 25 20’6” is 25 degrees, 20 minutes, and 6 seconds
- 4. Examples: 12.3 = 12 + 0.3(60)’ = 12 18’
- 5. Convert 200 40’ to a decimal:
- 6. One radian is the measure of a central angle whose arc length is equal to the radius.
- 7. A central angle θ (in radians) is: where s = arc length and r = radius Also, s = rθ
- 8. 1 revolution = 360 = 2π radians ½ revolution = 180 = π radians To convert:
- 9. Convert Convert -220 to radians (π). to degrees.
- 10. Convert Convert 196 to radians (decimal). 1.35 radians to decimal degrees.
- 12. Vertex at origin Initial ray on + x-axis Counterclockwise rotation is + Clockwise rotation is -
- 13. Two angles in std. position are coterminal if they have the same terminal ray. Each angle has infinitely many coterminal angles.
- 14. Find two angles, one + and one -, that are coterminal with π/4. Sketch all 3 angles.
- 15. Find two (+ and -) coterminal angles of 4π/3.