sec 42A intro to degree and radian measure.notebook
October 27, 2016
Angles and Their Measure
Te
rm
ina
l S
ide
• An angle can be generated by the rotation of two rays that share a fixed endpoint.
• Let one ray remained fixed to form the initial side of the angle
• Let the second ray rotate to form the terminal side.
Side
itial Vertex
In
Sid
nal
rmi
e
Te
Initial Side
Terminal Side
• An angle with its vertex at the origin and its initial side along the positive x­axis is said to be in standard position.
• If the terminal side of an angle in standard position coincides with one of the axes, the angle is called a quadrantal angle.
Initial Side
sec 42A intro to degree and radian measure.notebook
October 27, 2016
• If the rotation is in a counterclockwise direction, the angle formed is a positive angle.
• If the rotation is in a clockwise direction, the angle formed is a negative angle.
• Angle measures represent a distance, so the sign in front is a sign of direction, not measure.
The two most common units of measure for angles are Degrees and Radians.
Degree Measure:
1 degree = of a circle.
90o angle is a right angle
angles less than 90o are acute angles
angles greater than 90o are obtuse angles
sec 42A intro to degree and radian measure.notebook
October 27, 2016
Degrees, Minutes and Seconds
Fractional parts of angles are expressed in decimal form or in minutes and seconds.
Notation:
1o = 1 degree
1' = 1 minute
1" = 1 second
1 degree = 60 minutes = 3600 seconds
Example:
Convert to decimal degree form.
a) 245o10'
b) ­408o16'20"
sec 42A intro to degree and radian measure.notebook
October 27, 2016
Example:
Convert to DoM'S".
a) ­345.12o
b) 16.7865o
Radian Measure:
• The radian is based on the concept of a unit circle.
• To define what a radian is, we will use the central angle of a circle, an angle whose vertex is the center of the circle.
r
s = r
One Radian is the measure of a central angle θ that intercepts an arc s equal in length to the radius r of the circle.
θ
r
where θ is measured in radians.
sec 42A intro to degree and radian measure.notebook
October 27, 2016
Degrees vs. Radians
Since we know that 1 revolution = 360 o
2π radians = 360 degrees = 1 rev
and
π radians = 180 degrees
To convert from degrees to radians, multiply by:
To convert from radians to degress, multiply by:
Convert from Degrees to Radians. Show Work!
When converting from degrees to radians, all answers should ALWAYS be written in simplest rational form in terms of Pi.
No decimals, unless problem specifies!
sec 42A intro to degree and radian measure.notebook
Convert from Radians to Degrees. Show Work!
Homework:
Read section 4­2 and Do pg 238, #'s 2­8 even & 10­17 all
October 27, 2016