Unit Circle Discovery Activity
Our goals for this activity….
 I will have a completely filled-in unit circle to use as reference tool throughout the unit
 I can find the sin, cos, tan, csc, sec, cot of given angles without a calculator (but using my unit circle).
 I can evaluate the inverse trigonometric functions without a calculator (but using my unit circle).
Prerequisite Skills:
45-45-90 Right Triangles:
30-60-90 Right Triangles:
2x
600
450
x
x 2
x
300
450
x 3
x
Examples: Find all missing sides
450
300
. Check these with Mr. Hickerson or Mrs. Goranson
10
5
60
0
45
600
300
0
4
Drawing Angles on the coordinate plane: (Angles start on the positive x-axis and open counter clockwise)
450
900
1350
210 0
Now your ready….. (check your answers with Mr. Hickerson or Mrs. Goranson)
30 0
Complete the (x, y) coordinate for each angle measure in the unit circle. The common angles to know are multiples of 45
and multiples of 30. All answers should be simplified (which means the denominator should be rationalized)
Please check the first quadrant with me before you move to quadrants II, III, IV. (Two copies are provided, make
sure you have one that is 100% correct and neat)
Connection with Trig:
1. Draw the 45 degree triangle from your circle. Label all the sides.
2. Find the cos(45) using the definition of cosine (Hint: Use SOHCAHTOA)
Repeat 1&2 for angles 30,60.
Compare the (x,y) coordinates to the cosine and sine of the angle. How can you look at your unit circle and tell the
cos(135) ? What about sin(270)? Any ideas on tan(0)?
Practice: Use your unit circle to find the exact value of the following expressions:
1.
sin180o
2.
sin 225o
3.
cos 240o
4.
cos120o
5.
6.
tan 270o
7.
cot 0o
8.
sec150o
9.
sec 0o
10. csc 45o
11. csc 330o
 2 

 2
16. csc1 
 2

 2 
12. sin 1 


17. sec 1  

2 

3
1
13. sin  1

14. cos 1  


3

2 
tan 315o
15. tan 1 (0)