academy algebra ii/trig
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Academy Algebra II/Trig. Pre-Calculus (4.1) 7.1: Angles and Their Measure HW tonight: p.513 (11-22 all ) HW tomorrow: p.513 (24-62 even). Angles. The initial side of an angle coincides with the positive x-axis. - PowerPoint PPT PresentationTRANSCRIPT
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Academy Algebra II/Trig
Pre-Calculus (4.1)7.1: Angles and Their MeasureHW tonight: p.513 (11-22 all) HW tomorrow: p.513 (24-62 even)
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Angles The initial side of an angle coincides with
the positive x-axis. Positive angles are generated by a
counterclockwise rotation and a negative angle by a clockwise rotation.
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Coterminal Angles Angles with the same initial and terminal
sides are coterminal angles.
Alpha and beta arecoterminal angles.
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Radian Measure One radian is the measure of a central
angle that intercepts an arc s equal in length to the radius r of the circle.
r
r rs
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Radian Measure Because the circumference of the circle is
, it follows that a central angle of one full revolution corresponds to an arc length of . Therefore, radians corresponds to .
r2
r2 2360
2
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Radian Measure Other common angles:
4
6
2
3
Identify the Following angles:
0, , , and .2
3 2
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Determine the quadrant in which the angle lies. (The angle is given in radian measure.)
1.) 2.)
3.) -1 4.) 5.63
5.) 6.)
4
75
4
10
12
7
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Sketch the angle in standard position. Determine two coterminal angles in radian measure (one positive & one negative) for the given angle.
1.)
2.)
2
7
6
5
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Sketch the angle in standard position. Determine two coterminal angles in radian measure (one positive & one negative) for the given angle.
3.)
4.)
4
7
3
2
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Determine the quadrant in which the angle lies.
1.) 2.)
3.) 4.)
9.7 5.275
25.260 4.2
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Sketch the angle in standard position. Determine two coterminal angles in degree measure (one positive & one negative) for the given angle.
1.)
2.)
120
270
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Find (if possible) the complement and supplement of the angle.Two positive angles are complementary
if their sum is . Two positive angles are supplementary if their sum is .
1.) 2.)
3.) 3 4.) 1.5
2
12
6
5
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Find (if possible) the complement and supplement of the angle.
1.) 2.)
3.) 4.)
87 167
130 52
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Do Now: Sketch the angle in standard position. Determine two coterminal angles in degree measure (one positive & one negative) for the given angle.
1.)
2.)
114
445
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Convert degrees to radians
rad180
1
180rad 1
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Express the angle in radian measure as a multiple of pi. 1.) 2.)
3.) 4.)
315 120
270 144
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Convert the angle measure from degrees to radians. Round your answer to three decimal places. 1.) 2.)
52.46 7.83
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Express the angle in degrees.
1.) 2.)
3.) 4.)
12
7
9
6
1515
28
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Convert the angle measure from radians to degrees. Round your answer to three decimal places. 1.) 2.) 4.8
13
8
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Convert the angle to decimal form.60 minutes = 1 degree60 seconds = 1 minute
1.) 2.) 3.)'10275 '129 "36125
"'SMD
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Convert the angle to form.60 minutes = 1 degree60 seconds = 1 minute
1.) 2.)75.310 12.345
"'SMD
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Do Now: Round your answers to three decimal places. Convert the angle measure from degrees to radians. 1.) 2.)
3.) 4.) -0.48
54.0 395
5.6
Convert the angle measure from radians to degrees.
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Convert the angle to form.60 minutes = 1 degree60 seconds = 1 minute
3.) 4.) 355.0
"'SMD
7865.0
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Arc Lengthradians.in measured is wherers
240
4r
radians 3
4240
76.163
16
3
44
s
s
rs
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Find the radian measure of the central angle of a circle of radius r that intercepts an arc of length s.1.) r = 22 feet, s = 10 feet
2.) r = 80 km, s = 160 km
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Find the length of the arc on a circle of radius r intercepted by a central angle of .1.) r = 9 feet,
2.) r = 40 cm,
60
radians 4
3