HW 54 Answer Key
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Aim 55: How do we work with angles and coterminal angles?
Do Now: 90o
A) How many degrees are in a circle?
0o
360o
180o
B) Label the quadrants on the diagram.
270o
Angles in Standard Position
• An angle is in standard position if its vertex is located at the _____________ and one ray is on the ______________ x­axis. • The ray on the x­axis is called the ____________ ray and the other ray is called the _____________ ray. The angle is measured by the amount of rotation from the _________ side to the __________ side.
If measured in a counter­clockwise direction the measurement is ________.
If measured in a clockwise direction the measurement is __________. Key Angle Terms
Acute angles ­ measure between 0o and 90o (quadrant 1)
Obtuse angles ­ measure between 90o and 180o (quadrant 2)
Quadrantal angles ­ not "in" a quadrant, but on the axes
(0o, 90o, 180o, 270o, 360o)
1) In which quadrant do the following angles lie? a) 145 o b) 303o c) 412 o d) 270o
e) 240 o f) ­72 o
2) Angle DOG is in quadrant IV. It has a clockwise rotation of ­57 o . What is its counterclockwise rotation?
90o
180o
D
O
0o
360o
G
Angles of ­57 o and 303 o share the same initial and terminal rays, so they are called coterminal angles. 270o
Coterminal Angles
If two angles in standard position have the same terminal side, they are called coterminal angles.
Practice: Draw an angle with the given measure and name the quadrant in which the angle lies. State one coterminal angle for each.
3) 160o 4) ­125o 5) 180o 6) Which of the following angles is not coterminal to an angle that measures ­120 o?
a) ­480 o b) 60 o c) 240 o
d) 600 o
7) State the smallest positive coterminal angle of each of the following angles given in degrees. a) ­330
e) ­270
b) ­90
f) 45
c) ­180
d) ­315
g) 860
Sum it Up
An angle with counterclockwise rotation is ____________.
An angle with clockwise rotation is ___________. Coterminal angles have the same ____________ ray and _____________ ray. To find coterminal angles for one angle, just add or subtract multiples of ______.
If a positive and a negative angle are coterminal, the sum of the absolute values of their measures is 360o (or a ___________ of 360o)
Mad Minute:
Total: / 14 Determine the quadrant that each angle belongs in. If an angle is a quadrantal angle, write Q. 1. 450
2. ­450
3. 1250
4. 750
5. ­1000
6. 2700
7. 2580
8. ­1900
9. 5000
10. 4000
11. ­4000
12. ­100
13. 7200
14. 64.20