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