1. Trigonometric Functions: The Unit Circle (Section 4-2)

2. The Unit Circle
x2 + y2 = 1

3. Each value on the unit circle corresponds to a set of coordinates (x, y) = (cos, sin)

4. Determine the exact value of the six trig functions of the angle θ.
Example 1 θ

5. Determine the exact value of the six trig functions of the angle θ.
Example 2 θ

6. 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

7. A S C T ( , ) ( , ) ( , ) ( , ) ( , ) ( , ) ( , ) ( , ) ( , ) ( , )
(cos, sin) A
(0, 1) S
( , ) 1 3 -
( , ) 1 3 2 2 2 2
( , ) 2 2
( , ) 2 2 - 2 2 2 2
( , ) 3 1
( , ) 3 1 - 2 2 2 2
(-1, 0)
(1, 0) 2π π
( , ) 3 - 1
( , ) 3 - 1 - 2 2 2 2
( , ) 2 2
( , ) 2 2 - - - 2 2 2 2
( , ) 1 3
( , ) 1 3 - - - C 2 2 2 2
(0, -1) T

8. Find the point (x, y) on the unit circle that corresponds to the real number t.
Example 3

9. Find the point (x, y) on the unit circle that corresponds to the real number t.
Example 4

10. Find the point (x, y) on the unit circle that corresponds to the real number t.
Example 5

11. Evaluate the sine, cosine and tangent of the real number.
Example 6

12. Evaluate the six trig functions of the real number.
Example 7

13. Evaluate the trigonometric function using period as an aid
Evaluate the trigonometric function using period as an aid. (Add/ Subtract 2π)
Example 8

14. Evaluate the trigonometric function using period as an aid
Evaluate the trigonometric function using period as an aid. (Add/ Subtract 2π)
Example 9

15. Even and Odd Trig Functions
cos (-t) = cos t sec (-t) = sec t
Odd:
sin (-t) = - sin t csc (-t) = - csc t
tan (-t) = - tan t cot (-t) = - cot t

16. Use the value of the trig function to evaluate the indicated functions.
Example 10
a) sin (-t)
b) csc (-t)

17. Use the value of the trig function to evaluate the indicated functions.
Example 11
a) cos (-t)
b) sec (-t)

18. Use your calculator to evaluate the trigonometric function.
Example 12

19. Use your calculator to evaluate the trigonometric function.
Example 13

20. Use your calculator to evaluate the trigonometric function.
Example 14

21. HW #13 pg 275 (37 – 48 all, 51 – 67 odd)