LESSON ____ SECTION 4.2 The Unit Circle

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  ?

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

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

Special Right Triangles 30-60-90 30° 2 30° 60° Special Right Triangles 60° 1

Special Right Triangles 45-45-90 45° 1 45° 45° Special Right Triangles 1

Special Right Triangles 30-60-90 45-45-90 30° 45° 2 Special Right Triangles 1 45° 60° 1 1

( , ) ( , ) ( , ) ( , ) ( , ) ( , ) ( , ) ( , ) ( , ) ( , ) ( , ) ( , ) ( , ) ( , ) ( , ) ( , ) ( , ) ( , ) ( , ) ( , )

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

(0,1) (-1,0) (1,0) (0,-1)

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

Evaluate using the Unit Circle!

The Trig Ratios as Functions 1 -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

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

Memorize! 30° 45° 60° sin cos tan 1