7 1 measurement of angles
TRANSCRIPT
Objectives:
1. Measure angles in degrees and radians
2. Find coterminal angles
Trigonometry comes from Greek
words meaning “triangle
measurement.”
Has been used for centuries in
navigation and surveying.
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
Examples:
12.3 = 12 + 0.3(60)’ = 12 18’
Convert to a decimal:
200 40’
One radian is the measure of a
central angle whose arc length is
equal to the radius.
A central angle θ (in radians) is:
where s = arc length and r = radius
Also, s = rθ
1 revolution = 360 = 2π radians
½ revolution = 180 = π radians
To convert:
Convert -220 to radians (π).
Convert to degrees.
Convert 196 to radians (decimal).
Convert 1.35 radians to decimal
degrees.
Vertex at origin
Initial ray on + x-axis
Counterclockwise rotation is +
Clockwise rotation is -
Two angles in std. position are
coterminal if they have the same
terminal ray.
Each angle has infinitely many
coterminal angles.
Find two angles, one + and one -,
that are coterminal with π/4. Sketch
all 3 angles.
Find two (+ and -) coterminal angles
of 4π/3.