Name:_______________________
Class Period:__________________
Gifted/Accelerated Math 3
Adapted from Acc Math 3 State Task Unit 4
Right Triangles and Coordinates on the Unit Circle
1. The circle to the right is referred to as a “unit circle.” Why is it called a
unit circle?
2. What angles have a reference angle of 30 o. Using trigonometric ratios, what are the coordinates of
where each angle intersects the circle? How do these coordinates relate to the coordinates of the
30o angle?
 (angle measure)
x-coordinate
y-coordinate
30 o
4. What angles have a reference angle of 45 o. Using trigonometric ratios, what are the coordinates of
where each angle intersects the circle? How do these coordinates relate to the coordinates of the
45o angle?
 (angle measure)
x-coordinate
y-coordinate
45 o
5. What angles have a reference angle of 60 o. Using trigonometric ratios, what are the coordinates of
where each angle intersects the circle? How do these coordinates relate to the coordinates of the
60o angle?
 (angle measure)
60 o
x-coordinate
y-coordinate
6. There are a few angles for which we do not draw right triangles even though they are very
important to the study of the unit circle. These are the angles with terminal sides on the axes.
What are these angles? What are their coordinates that fall on the unit circle?
 (angle measure)
x-coordinate
y-coordinate
7. Moving the triangle onto the unit circle allows us to represent the trigonometric relationships in
terms of x and y. Express each of the ratios in terms of x and y.
r

x
sin  
1
y

x
cos 
tan  
sin  
y
cos 
tan  
Therefore, we can tell from the unit circle that the sin  = _________ and the cos  = _________.
*This is true for all angles represented on the unit circle.
-----------------------------------------------------------------------------------------------------------------------Practice:
Evaluate the trigonometric function. All answers must be exact. Assume all angles not expressed in
degrees are expressed in radians.
1.
cos 60o
2.
sin 135o
3.
cos 210o
4.
tan -30o
5.
cos 270o
6.
sin -90o
7.
tan 90o
8.
sin 1320o
9.
cos -675o
AM3 - Homework: Unit Circle
1.
Name: __________________
Date: ___________________
At this point we have learned degrees, sine and cosines of angles that fall on the unit circle.
We have also observed patterns in the coordinates on the unit circle.
Fill in everything that you know about the Unit Circle.
Fill in the blanks with the appropriate angle in degrees.
2.
The sin of __________ and __________ is ½.
3.
The cos of __________ and __________ is 0.
4.
The cos 135o and 225o is __________.
5.
The sin of __________ and __________ is 
6.
The cos of __________ and __________ is ½.

7.
The sin of 210o and 330o is __________.
3
.
2
-----------------------------------------------------------------------------------------------------------------------For Questions 8-19, evaluate the trigonometric function based on your knowledge of the unit circle.
All answers must be exact.
8.
cos 135
9.
sin 330
10.
cos270
11.
tan 675
12.
cos 960
13.
cos  330
14.
sin 300
15.
tan 4320
16.
cos 1620
17.
cos  90
18.
sin 1890
19.
tan  600
-----------------------------------------------------------------------------------------------------------------------Name the quadrant in which  lies given the following information:
20. cos   0 and sin   0 ______
21. tan   0 and sin   0 ______