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COTERMINAL ANGLES
INTRO TO COLLEGE MATH
Consider the angle 30 , in standard position.
Now consider the angle
degrees.
. We can think of this angle as a full rotation
, plus an additional 30
What do you notice about the terminal ray of each angle?
Formally, we say that the angles share the same terminal side. Therefore we call the angles coterminal .
Not only are these two angles coterminal, but there are infinitely many angles that are coterminal with
these two angles. We can spin in both the positive and negative direction, as many times as we would
like.
Exercise #1: Name four more angles that are co-terminal with the 30 shown above.
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Exercise #2: Is the following angle co-terminal with
?
Exercise #3: Is the following angle co-terminal with
405
?
y
45
x
Exercise #4: Is the following angle co-terminal with
?
Coterminal Angles: A set of coterminal angles are angles with the same terminal side but expressed
differently, such as a different number of complete rotations around the unit circle or angles being
expressed as positive versus negative angle measurements.
Exercise #5: What do you notice about the sum of the (absolute values) of the angles in exercise #4?
Exercise #6: Name a negative coterminal angle to
.
Exercise #7: Name three different coterminal angles to 70 .
Exercise #8: Name the angle associated with 10 on a standard clock.
Exercise #9: Name the angle associated with 2 on a standard clock.
Exercise #10: Name three coterminal angles associated with 2 on a standard clock.
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COTERMINAL ANGLES
INTRO TO COLLEGE MATH HOMEWORK
1. 1. Is
3. Is
co-terminal with
?
co-terminal with
?
2. Is
co-terminal with
?
4. Is
co-terminal with
?
For each diagram, name the angle in 3 ways. At least one way should use negative degrees.
5.
6.
7.
8.
9. Name the angle of the 8 on a standard clock two different ways.
10. How many rotations is
?
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