1. LESSON ____ SECTION 4.2
The Unit Circle

2. The Unit Circle: Center: (0,0) Radius: Equation: 1 unit x2 + y2 =1 -1
Circumference?
Arc length for a central angle of ?
Arc length for a central angle of  ?

3. t Imagine the real number line is wrapped around the unit circle.
Each real number t on that line corresponds to a point (x,y) in the coordinate plane. y x t

4. The Six Trigonometric Functions
(x, y)
Remember:
“SOH CAH TOA” t 1 y t x
The Six Trigonometric Functions
Reciprocal Functions

5. Special Right Triangles
30° 2
30°
60°
Special Right Triangles
60° 1

6. Special Right Triangles
45° 1
45°
45°
Special Right Triangles 1

7. Special Right Triangles
30°
45° 2
Special Right Triangles 1
45°
60° 1 1

8. ( , )
( , )
( , )
( , )
( , )
( , )
( , )
( , )
( , )
( , )
( , )
( , )
( , )
( , )
( , )
( , )
( , )
( , )
( , )
( , )

10. (x, y )
sin t
(0,1)
(-1,0)
(1,0)
(0,-1)

11. (0,1)
(-1,0)
(1,0)
(0,-1)

12. (x, y )
cos t
(0,1)
(-1,0)
(1,0)
(0,-1)

13. Evaluate using the Unit Circle!

14. The Trig Ratios as Functions1 -1
The Trig Ratios as Functions
Domain of sine & cosine:
Range:
(-∞,∞)
[-1, 1]
Sine & cosine are examples of “periodic functions”
sin (π/4) =
The values cycle “periodically”
sin (π/4+ 2π) =
How long does it take to cycle? 2π
This number is called the “period” of the function.
sin (π/4+ 4π) =
Is sine an even or odd function?
Definition of a Periodic Function
ODD
Is cosine an even or odd function?
EVEN

15. Know how to evaluate trig functions for special angles
30°
45°
60°
sin
cos
tan

16. Memorize!
30°
45°
60°
sin
cos
tan 1