
Finding Angles of Rotation
Presentation
•
Mathematics
•
12th Grade
•
Hard
Joseph Anderson
FREE Resource
13 Slides • 15 Questions
1
2
The word trigonometry means “measurement of triangles.”
An angle is determined by rotating a ray (half-line) about its endpoint.
3
4
negative angles --> clockwise rotation
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6
Multiple Choice
What does the word "trigonometry" literally mean?
Rotation of lines
Calculation of angles
Measurement of triangles
Study of circles
7
Multiple Choice
In standard position, an angle's vertex is located:
At any point on the coordinate plane
At the origin (0, 0)
On the x-axis
On the y-axis
8
Multiple Choice
Which statement about angle rotation is correct?
Positive angles rotate clockwise
Negative angles rotate counterclockwise
Positive angles rotate counterclockwise
All angles rotate in the same direction
9
Multiple Choice
Coterminal angles are angles that:
Have the same length
Form a right angle
Rotate in opposite directions
Have the same initial and terminal sides
10
Multiple Choice
What describes the initial side of an angle in standard position?
Located on the negative x-axis
Located on the positive y-axis
Located on the positive x-axis
Can be anywhere on the coordinate plane
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Radian Measure
Radian: An angle measurement based on the radius
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ways of measuring angles
1- Degree Measure:
Full circle = 360 degrees
Right angle = 90 degrees
Straight angle = 180 degrees
2- Radian Measure:
Full circle = 2π radians
Half circle = π radians
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A radian is the angle where the arc length equals the radius length
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Example 1: Finding Coterminal Angles
Add or subtract 2π to get coterminal angles Formula: θ ± 2π
Solve: Determine two coterminal angles (one positive and one negative) for each angle.
a) θ = π/4
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Multiple Select
Determine two coterminal angles (one positive and one negative) for each angle. (Choose 2 answers)
38π
−37π
35π
−35π
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Multiple Select
Determine two coterminal angles (one positive and one negative) for each angle. (Choose 2 answers)
4π
−47π
45π
−45π
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18
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Multiple Choice
Find (if possible) the complement of 6π
5π
3π
65π
none
20
Multiple Choice
Find (if possible) the supplement of 6π
5π
32π
65π
none
21
Multiple Choice
Find (if possible) the complement of 65π
5π
32π
65π
none
22
Multiple Choice
Find (if possible) the supplement of 65π
6π
4π
3π
none
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A second way to measure angles is in degrees, denoted by the symbol °.
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25
Multiple Choice
Convert each degree measure to radian measure as a multiple of π. Do not use a calculator.
a) 60⁰
π/4
π/3
π/6
π/9
26
Multiple Choice
Convert each degree measure to radian measure as a multiple of π. Do not use a calculator.
a) 320⁰
14π/9
16π/9
11π/9
17π/9
27
Multiple Choice
Convert each radian measure to degree measure. Do not use a calculator.
a) π / 6
30°
60°
45°
55°
28
Multiple Choice
Convert each radian measure to degree measure. Do not use a calculator.
a) 5π / 3
270°
320°
280°
300°
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