1. Build and Use Unit Circle
(Section 13-3 Alg 2)

2. x y
Trig functions of an angle in standard position: For any angle in standard position with measure θ, a point P(x,y) on its terminal side, and r= , the trigonometric functions of θ are as follows.
sin θ = cos θ = tan θ =
csc θ = sec θ = cot θ =

3. Trig identities:
csc = sec=
tan = cot =

4. x y 180°/ π 360°/2 π sin cos tan csc sec cot 90°/ 270°/ (1, 0) (0, 1)
(0, -1)
(-1, 0)
Special Values:
(cos, sin)
180°/ π
360°/2 π
sin
cos
tan
csc
sec
cot
90°/
270°/

5. State whether the value of each function is positive, negative, zero or undefined.
Example 1: sin (-135°) Example 2: cos 405°
Example 3: tan 315° Example 4: cot 2π

6. Example 5: csc Example 6: sec
State whether the value of each function is positive, negative, zero or undefined.
Example 5: csc
Example 6: sec
Example 7: tan 90° Example 8: cot (-45°)

7. 30° 45° 60° II I 120° 90° 2 Sin, csc + (students) 60°
All + 1
135°
45°
150°
30°
180°,π
0°,2π IV
45° 1
210°
330°
225°
315°
60° 1 2
tan, cot + (take)
240°
300°
cos, sec + (calculus)
270°
III

8. Find the exact value of each trig function.

9. Find the exact value of each trig function.

10. Find the exact value of each trig function.

11. Find the exact value of each trig function.

12. Find the exact value of each trig function.

13. Find the exact value of each trig function.

14. Find the exact value of each trig function.

15. Find the exact value of each trig function.

16. Find the exact value of each trig function.

24. 120°
90°
60°
135°
45°
150°
30°
180°,π
0°,2π
210°
330°
225°
315°
240°
300°
270°

25. II I
120°
90°
60°
135°
45°
150°
30°
180°,π
0°,2π
210° IV
330°
225°
315°
240°
300°
270°
III

26. 30°
45°
60°
90°
120°
135°
150°
180°,π
210°
225°
240°
270°
300°
315°
330°
0°,2π
All +
tan, cot + (take)
cos, sec + (calculus) I
III II IV
Sin, csc + (students)
sin, csc + (students)

27. 60°
45°
30°

28. 60° 1 2
45° 1
30° 2 1

29. 30° 45° 60° CLASSROOM COPY RETURN AT END OF CLASS II I 120° 90° 2
Sin, csc + (students)
60°
sin, csc + (students)
All + 1
135°
45°
150°
30°
180°,π
0°,2π
45° 1
210° IV
330°
225°
315°
60° 1 2
tan, cot + (take)
240°
300°
cos, sec + (calculus)
270°
III

30. 30° 45° 60° CLASSROOM COPY RETURN AT END OF CLASS II I 120° 90° 2
Sin, csc + (students)
60°
sin, csc + (students)
All + 1
135°
45°
150°
30°
180°,π
0°,2π
45° 1
210° IV
330°
225°
315°
60° 1 2
tan, cot + (take)
240°
300°
cos, sec + (calculus)
270°
III

31. 30° 45° 60° CLASSROOM COPY RETURN AT END OF CLASS II I 120° 90° 2
Sin, csc + (students)
60°
sin, csc + (students)
All + 1
135°
45°
150°
30°
180°,π
0°,2π
45° 1
210° IV
330°
225°
315°
60° 1 2
tan, cot + (take)
240°
300°
cos, sec + (calculus)
270°
III

32. 30° 45° 60° CLASSROOM COPY RETURN AT END OF CLASS II I 120° 90° 2
Sin, csc + (students)
60°
sin, csc + (students)
All + 1
135°
45°
150°
30°
180°,π
0°,2π
45° 1
210° IV
330°
225°
315°
60° 1 2
tan, cot + (take)
240°
300°
cos, sec + (calculus)
270°
III