Do Now: Graph the equation: X 2 + y 2 = 1 Draw and label the special right triangles What happens when the hypotenuse of each triangle equals 1?

PRE-CALC: 4.2: TRIG FUNCTIONS: THE UNIT CIRCLE ALGEBRA II HONORS

Trigonometry The word trigonometry means measurement of triangles. Initially trigonometry dealt with the relationships among the sides and angles of triangles. y x r

Trigonometry y x r

SIX TRIGONOMETRIC FUNCTIONS Sine (sin) Cosine (cos) Tangent (tan) Cosecant (csc) Secant (sec) Cotangent (cot)

UNIT CIRCLE: X 2 + Y 2 = 1 (1,0) (0,1) (0,-1) (-1,0)

UNIT CIRCLE: X 2 + Y 2 = 1 x y r (x,y) (0,1) (1,0) (0,-1) (-1,0)

UNIT CIRCLE: X 2 + Y 2 = 1 x y 1 (x,y) (0,1) (1,0) (0,-1) (-1,0)

Unit Circle Trig y x 1

UNIT CIRCLE: X 2 + Y 2 = 1 1 (0,1) (1,0) (0,-1) (-1,0)

UNIT CIRCLE Let the radius = 1. Graph x 2 + y 2 = 1 Find the (x, y) coordinates using special right triangle ratios for (1,0) (0,1) (-1,0) (0,-1)

UNIT CIRCLE Find all the (x, y) coordinates using special right triangle ratios for (1,0) (0,1) (-1,0) (0,-1)

UNIT CIRCLE Let the radius = 1. Find the (x, y) coordinates using special right triangle ratios for (1,0) (0,1) (-1,0) (0,-1)

UNIT CIRCLE Let the radius = 1. Find the (x, y) coordinates using special right triangle ratios for (1,0) (0,1) (-1,0) (0,-1)

UNIT CIRCLE Let the radius = 1. Find the (x, y) coordinates using special right triangle ratios for (1,0) (0,1) (-1,0) (0,-1)

UNIT CIRCLE Let the radius = 1. Find the (x, y) coordinates using special right triangle ratios for (1,0) (0,1) (-1,0) (0,-1)

UNIT CIRCLE: FOR EACH POINT ON THE UNIT CIRCLE LABEL THE ORDERED PAIR (COS, SIN) AND THE ANGLE IN DEGREES AND RADIANS.

Closing: What special triangles did we use to help us learn the unit circle?

Homework: worksheet

DO NOW: FOR EACH POINT ON THE UNIT CIRCLE LABEL THE ORDERED PAIR (COS, SIN) AND THE ANGLE IN DEGREES AND RADIANS.

UNIT CIRCLE WORKSHEET

Practice

Trigonometry y x 1

Trigonometry: Given that cos = x and sin = y Find a new way to write tan, cot, sec, and csc.

TRIG FUNCTIONS: UNIT CIRCLE (reciprocal of cosine) (reciprocal of sine)

Practice

Homework: Packet 1-28