Do Now:

• Graph the equation:

X2 + y2 = 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

x

y

r

x

r

y

)tan(

)cos(

)sin(

r

Trigonometry

y

x

y

x

x

y

x

r

r

x

r

y

)cot( )tan(

)sec( )cos(

y

r)csc( )sin(

r

SIX TRIGONOMETRIC FUNCTIONS

• Sine (sin)• Cosine (cos)• Tangent (tan)• Cosecant (csc)• Secant (sec)• Cotangent (cot)

UNIT CIRCLE: X2 + Y2 = 1

(1,0)

(0,1)

(0,-1)

(-1,0)

UNIT CIRCLE: X2 + Y2 = 1

x

yr

(x,y)

(0,1)

(1,0)

(0,-1)

(-1,0)

UNIT CIRCLE: X2 + Y2 = 1

x

y1

(x,y)

(0,1)

(1,0)

(0,-1)

(-1,0)

Unit Circle Trig

y

x

y

x

x

y

x

x

y

)cot( )tan(

1)sec(

1)cos(

y

1)csc(

1)sin(

1

UNIT CIRCLE: X2 + Y2 = 1

1)sin,(cos

cos

sin

(0,1)

(1,0)

(0,-1)

(-1,0)

UNIT CIRCLE

• Let the radius = 1.• Graph x2 + y2 = 1• Find the (x, y)

coordinates using special right triangle ratios for 45-45-90.

(1,0)

(0,1)

(-1,0)

(0,-1)

UNIT CIRCLE

• Find all the (x, y) coordinates using special right triangle ratios for 45-45-90.

(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 30-60-90.

(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 30-60-90.

(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 30-60-90.

(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 30-60-90.

(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 radians degrees cos sin tan sec csc cot 1. 0

2.

6

3.

4

4.

3

5.

2

6.

3

2

7.

4

3

8.

6

5

UNIT CIRCLE WORKSHEET9.

10.

6

7

11.

4

5

12.

3

4

13.

2

3

14.

3

5

15.

4

7

16.

6

11

17. 2

radians degrees cos sin tan sec csc cot

Practice

Practice

Practice

Trigonometry

y

x

y

x

x

y

x

x

y

)cot( )tan(

1)sec(

1)cos(

y

1)csc(

1)sin(

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)

cos

sintan

cos

1sec

sin

1csc (reciprocal of sine)

sin

coscot

Practice

Homework:

• Packet • 1-28