Download Goal: Find the exact values of the six trigonometric

Honors Algebra 2
Unit Circle Day 2
Name_________________
Date__________________
Goal: Find the exact values of the six trigonometric functions of special angles.
Let’s summarize what you’ve learned about trigonometric functions on the unit circle:
1. A unit circle has a radius length of _______.
2. On the unit circle, each x-coordinate represents the _________ ratio of that measure.
3. On the unit circle, each y-coordinate represents the _________ ratio of that measure.
4. Angles that have a positive measure rotate in a ________________________ direction.
5. As a measure increases from zero degrees to 90 degrees, its sine ratio ______________
and its cosine ratio ____________________.
6. As a measure increases from 90 degrees to 180 degrees, its sine ratio ______________
and its cosine ratio ___________________.
7. As a measure increases from 180 degrees to 270 degrees, its sine ratio _____________
and its cosine ratio ____________________.
8. As a measure increases from 270 degrees to 360 degrees, its sine ratio _____________
and its cosine ratio _____________________.
9. The highest value for a cosine ratio is ________.
10. The lowest value for a cosine ratio is _________.
11. The highest value for a sine ratio is _________.
12. The lowest value for a sine ratio is _________.
13. Sine (and therefore its reciprocal, cosecant) is positive in which quadrants? ________
14. Cosine (and therefore its reciprocal, secant) is positive in which quadrants? ________
15. Tangent (and therefore its reciprocal, cotangent) is positive in which quadrants? ________
16. In which quadrant(s) are all trigonometric functions positive? ___________
17. Illustrate the mnemonic device “All Students Take Calculus.”
Honors Algebra 2
Unit Circle Day 2
Name_________________
Date__________________
18. Tell whether the value of each trigonometric function is positive, negative, zero, or
undefined.
a) sin 2
b) cos

4
c) tan 315 ˚
19. In which quadrant(s) are both of the following statements true?
a) cos θ > 0 and sin θ < 0
b) sin θ < 0 and tan θ > 0
c) cos θ < 0 and tan θ < 0
20.

radians is ______ degrees.
4

radians, then the angle’s
4
radian measure has the number ____ in the denominator. These angles have related x- and ycoordinates. The x-coordinates have the absolute value of ______. The y-coordinates have the
absolute value of ______.
21. If an angle on the unit circle has a reference angle measuring
22.

radians is _____ degrees.
6

radians, then the angle’s
6
radian measure has the number ____ in the denominator. These angles have related x- and ycoordinates. The x-coordinates have the absolute value of ______. The y-coordinates have the
absolute value of ______.
23. If an angle on the unit circle has a reference angle measuring
24.

radians is ______ degrees.
3

radians, then the angle’s
3
radian measure has the number ____ in the denominator. These angles have related x- and ycoordinates. The x-coordinates have the absolute value of ______. The y-coordinates have the
absolute value of ______.
25. If an angle on the unit circle has a reference angle measuring
Honors Algebra 2
Unit Circle Day 2
Name_________________
Date__________________
26. Draw just the first quadrant of the unit circle below. You need to memorize it!
27. Without looking at the unit circle, determine each exact value.
a) cos
5
6
Thought process:
The denominator is _____, so it is related to _______, which has the coordinates _________.
5

is bigger than
but smaller than  so it is in the _______ quadrant.
6
2
The coordinates of
b) sin
5
:
6
cos
5
=
6
7
4
Thought process:
The denominator is _______, so it is related to ______, which has coordinates _____________
7
is bigger than ______ but smaller than _____ so it is in the _____ quadrant.
4
The coordinates of
7
:
4
sin
7
=
4
Honors Algebra 2
Unit Circle Day 2
Name_________________
Date__________________
Use the unit circle and your knowledge of trig functions to find the exact simplified
answer for the following problems.
9 

 tan

4 

1.
cot 45o 
 sin 7 
2. 2
sin  
 6 
   4   5 

3.  tan    cot
   cot

3 
3  
3 

   2 

 cos    sin

3 
3 

4.
7 

 sec

4 

  5 
4 

5.  cot  sec
 tan

3 
3 
3 

   

6.  tan  csc 
6 
3

2
Honors Algebra 2
Unit Circle Day 2
 3 
7.  sin

2 

Name_________________
Date__________________
3 

8. cos 60 o    cos 
2 

2
Now it’s your turn!
Use the unit circle and your knowledge of trig functions to find the exact simplified
answer for the following problems.
7 

o
 csc 
  sec 45 
2
2
   5 
2 

1.  cos    sin
2. 


3 
3 


 sec 
3

11 

3.  cos

6 

2
5  
3 

4.  tan
   tan

4  
4 

Honors Algebra 2
Unit Circle Day 2
Name_________________
Date__________________
   5 

2
5. sec     csc    sec

2 
6 

5 

 tan

6 

6.
11 

 cot

6 

  

7.  sec    csc 
6 
4



8.  cos   sin 
4

2
2
4  
7 

9.  cos
   sin

3  
4 

2
2
2
5   11 

11.  cot
  sec

3  
6 

3