1 .edu
Homework: 2.1: 3, 4a, 6-8, 23-33 odd, 37, 38, 43, 44, 48-50, 53, 54, 58, 71-78, 91, 92, 101, 102
Read Section 2.2
Terminology
[pic]
Initial side
Terminal side
Vertex
Direction in standard position
[pic]
Drawing Angles: (Examples in various Quadrants)
DEGREE MEASURE
One full revolution corresponds to 2π radians or 360º.
[pic] [pic]
Example: Convert 19.256º to Degrees minutes seconds
Example: Convert 53º23’15’’ to decimal degrees
DEF: Radian
One radian is the measure of a central angle that intercepts an arc s equal in length to the radius of a circle
Common angles:
Right Straight Common
IMPORTANT: Any angle measured in degrees MUST have a degree symbol. An angle without a º in ALWAYS in radians!!!
180º = π radians
Converting between degrees and radians
a) º ( radians: multiply by [pic]
b) radians ( º : multiply by [pic]
Example: Convert the following to Radians
a) 120º b) -20º
c) 240º d) 165º
e) [pic]º f) [pic]
NOTE: All answers should be given as exact fractions (NOT DECIMALS). Do not approximate π.
Example: Convert the following to Degrees:
a) [pic] b) [pic]
c) [pic] d) 27
On Calculator:
From Radians to Degrees
• Put Calculator in Degree Mode
• Input (angle)r
From Degrees to Radians
• Put calculator in Radian Mode
• Input (angle)°
If you divide by π ( Frac will give you the fraction coefficient.
(DMS converts to Degrees, Minutes, Seconds
Sketch the following angles. (Note you must carefully watch the mode!)
[pic] [pic]
[pic] [pic]
10 10°
Watch out for common mistakes! If the angle is negative, you must draw it clockwise. If the magnitude angle is greater than 2π, you must draw cycles around. If there is no degree symbol, the angle MUST be in radians!
ACR LENGTH: [pic]
Note: θ must be in radians!!! Units of s and r macth.
Example: A circle has a diameter of 10 inches. Find the length of the arc intercepted by an angle of 120º
Example: Find the measure of the central angle of a circle of radius r = 20 ft that intercepts an arc of length s = 100 ft
Example: You wish to cut a piece of pizza from a 12 inch pizza with the crust measuring 4.7 inches. In order to cut your pizza accurately, you needs to find the measure of the angle formed by the two non-crust sides of the pizza. Find the measure of the angle in degrees of the angle formed by the two non-crust sides of the pizza. Give your answer accurate to 4 decimal places.
Example: As the large hand on a circular clock moves from 12:40 pm to 1:00 pm it sweeps out a distance of 18 in. How big is diameter of the clock?
Distance between cities: The latitude of a location L is the angle formed by a ray drawn from the center of the Earth to the equator and a ray drawn from the center of the Earth to L.
Example: Charleston, West Virginia is due west of New Orleans, Louisiana. Find the distance between Charleston (35º30’ north latitude) and New Orleans (29º30’ north latitude). Assume the radius of the earth is 3960 miles.
Watch out for common mistakes! The angle MUST be in radians BEFORE plugging into the formula.
You need to convert angles to degrees AFTER using formula.
Always include units!
Review:
Angle conversions
180º = π radians
[pic] [pic]
Example: Convert 12º15’45” to radians
Example: Convert [pic]to degrees, minutes seconds
................
................
In order to avoid copyright disputes, this page is only a partial summary.
To fulfill the demand for quickly locating and searching documents.
It is intelligent file search solution for home and business.