8-20-14 T1.2c To Calculate Reference Angles
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1 8-20-14 T1.2c To Calculate Reference Angles “And then one of the little kids shined his flashlight into the corner of the basement, and there they saw these strange jars…Some said
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8-20-14 T1.2c To Calculate Reference Angles. “And then one of the little kids shined his flashlight into the corner of the basement, and there they saw these strange jars…Some said ‘creamy’, some said ‘crunchy’…”. Active Learning Assignment Questions?. An Astronaut’s View of Earth. - PowerPoint PPT Presentation
Transcript of 8-20-14 T1.2c To Calculate Reference Angles
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8-20-14
T1.2c To Calculate Reference Angles
“And then one of the little kids shined his flashlight
into the corner of the basement, and there they saw these strange jars…
Some said ‘creamy’, some said ‘crunchy’…”
2An Astronaut’s View of Earth
Active Learning Assignment Questions?
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START COPYING:
•Reference Angle: Given angle Ө (theta), the reference
angle, Ө’ (theta prime) is one whose initial side is on the
x axis and shares the same terminal side.
•The reference angle is never more than 90° and always
positive .
•In Quadrant I the angle and it’s reference have the
same initial side and same terminal side.
•In Quadrants II & III, the initial side is on the
NEGATIVE X axis and the terminal sides are the same.
•In Quadrant IV, the initial side is on the POSITIVE X
axis and the terminal sides are the same.
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In reality, it represents the space between the terminal side and the x axis. (almost absolute value definition!)
Let’s try:
1. 57
3. 204
2. 135
4. 326 We can draw them, but how can we find their reference angle measure?
I
IVIII
II
57°
45°
24°
34°
0°180°360°
57135
204326
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I
IVIII
II
321 39°
360
321
39°
Find the reference angle:
0°180°360°
321
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I
IVIII
II
152 37 27 23
180
152 37
27 23
Find the reference angle:
0°180°360°
179 60 152 37
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I
IVIII
II
588
Coterminal Angle?
588° - 360° = 228°
48°
Find the reference angle:
0°180°360°
228°
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I
IVIII
II259 79°
Or, use Coterminal Angles:
-259° + 360° = 101°
There are two ways to do this:
Count degrees backwards (-90°, -180°, -270°, etc)
Find the reference angle:
0°180°360°
Joke break: What lies on the bottom of the ocean and twitches?
A nervous wreck
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I
IVIII
II8
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First, write the quadrangle angles in π radians.
Then change to a common denominator.
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Find the reference angle:
0π2π
7
78
7
3.5
7
2
3
2
10.5
7
14
7
10
I
IVIII
II
11
6
6
Find the reference angle:
0π2π
6
6
11
6
1
6
3
6
2
3
2
9
6
I
IVIII
II
10
17
7
17
Find the reference angle:
0π2π
17
17
10
17
34
17
8.5
17
2
3
2
25.5
17
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Active Learning Assignment:Handout 1-16
