AM3: Angles on the Coordinate Plane
Name: ______________________
1. On a coordinate plane, positive angles rotate in a ________________ direction, while negative
angles rotate in a ________________ direction.
Fill in the blanks using the following words (words can be used more than once if necessary):
positive x –axis
negative x-axis
positive y-axis
negative y-axis
2. The terminal side of the angle 270 o falls on the ________________.
3. The initial side of the angle 180 o lies on the ________________.
4. The terminal side of the angle -90 o falls on the ________________.
5. The terminal side of the angle 180 o and -180 o falls on the ________________.
6. The terminal side of the angle 0 o, 360 o, and -360 o falls on the ________________.
True/False: Are the following angles coterminal?
7. 30 o and 750 o ______
9. 60 o and 240 o ______
8. 47 o and -493 o ______
10. 190 o and -2690 o ______
Determine the coterminal angle that lies between
and
for each angle.
11. 945o
______
13. 1500o
12. -950o
______
14. -1413o ______
______
Draw an angle with the given measure in standard position.
15. -210 o
16. 190 o
17. -50 o
For Questions 18-23, determine the value of the variable in the given diagram. Round all
answers to the nearest hundredth (two decimal places). Hints are given in Questions 1 & 2.
18.
19.
20.
4
10
23
a
c
19
45
52
b
 sin 52 
a
10
____ 45 

21.
b
4
22.
23.
p
n
60
22
m
25
17
10
34
------------------------------------------------------------------------------------------------------------------------------24.
A 12-foot ladder is leaning against a building and is resting on flat ground. If the ladder
creates a 65 angle with the ground, how far is the base of the ladder from the base
of the building? Round your answer to the nearest foot.
------------------------------------------------------------------------------------------------------------------------------25.
SLIDE
Steps to
top of slide
At a local corn maze attraction, a slide is constructed
using a long, straight tube (see left). If the slide
makes a 35 angle with the ground, and the tube is
100 feet long, approxmiately how high above the
ground does the slide start? Round to the nearest
tenth of a foot (one decimal place).
------------------------------------------------------------------------------------------------------------------------------Consider point P on the coordinate plane to the right.
26.
What one-line calculation could be done to find the
x-coordinate of point P?
27.
What one-line calculation could be done to find the
y-coordinate of point P?
28.
Combine your answers from Questions 14 & 15 to write
the ordered pair for the location of point P.
y-axis
P
1

x-axis
Answers:
1. counter clockwise, clockwise 2. Negative y-axis 3. Positive x-axis 4. Negative y-axis
5. Negative x-axis 6. Positive x-axis 7. Yes 8. No 9. No 10. Yes 11. 225 o
12. 130 o 13. 60 o 14. 27 o
15.
16.
17.
4
2
2
-5
18. 7.88
24. 5 feet
4
4
2
5
-5
-5
5
5
-2
-2
-2
-4
-4
-6
-6
-4
-6
19. 2.83
20. 7.49
21. 13.98
22. 15.76
23. 5
25. 57.4 feet 26. cos 
27. sin  28. (cos  , sin  )