12X1 T05 03 graphing inverse trig (2011)

Graphing Inverse Trig Functions

Graphing Inverse Trig Functions

3

sin5 e.g 1 xyi

Graphing Inverse Trig Functions

Domain:

3

sin5 e.g 1 xyi

13

1 x

33 x

Graphing Inverse Trig Functions

Domain:

Range:

3

sin5 e.g 1 xyi

13

1 x

252

y

33 x

25

25

y

Graphing Inverse Trig Functions

Domain:

Range:

3

sin5 e.g 1 xyi

13

1 x

252

y

y

x-3 3

25

25

33 x

25

25

y

Graphing Inverse Trig Functions

3sin5 1 xy Domain:

Range:

3

sin5 e.g 1 xyi

13

1 x

252

y

y

x-3 3

25

25

33 x

25

25

y

21 3tan xyii

21 3tan xyii

Domain:

3303 2

xx

21 3tan xyii

Domain:

Range:

3303 2

xx

0 0tan,3 1

yx

21 3tan xyii

Domain:

Range:

3303 2

xx

0 0tan,3 1

yx

0 0tan,3 1

yx

21 3tan xyii

Domain:

Range:

3303 2

xx

0 0tan,3 1

yx

0 0tan,3 1

yx

3

3tan,0 1

yx

21 3tan xyii

Domain:

Range:

3303 2

xx

0 0tan,3 1

yx

0 0tan,3 1

yx

3

3tan,0 1

yx

30

y

21 3tan xyii

Domain:

Range:

3303 2

xx

0 0tan,3 1

yx

y

x

3

0 0tan,3 1

yx

3

3tan,0 1

yx

30

y

3 3

21 3tan xyii

21 3tan xy

Domain:

Range:

3303 2

xx

0 0tan,3 1

yx

y

x

3

0 0tan,3 1

yx

3

3tan,0 1

yx

30

y

3 3

xyiii sinsin)( 1

xyiii sinsin)( 1

Domain:

all real x1sin1 x

xyiii sinsin)( 1

Domain:

all real x

Range:

1sin1 x

22

y

xyiii sinsin)( 1

Domain:

all real x

Range:

1sin1 x

22

yy

x

2

2

xyiii sinsin)( 1

xy sinsin 1

Domain:

all real x

Range:

1sin1 x

22

yy

x

2

2

xyiv 1sinsin)(

xyiv 1sinsin)(

Domain: 11 x

xyiv 1sinsin)(

Domain:

Range:

11 x

1 2

sin

1sinsin,1when 1

yx

xyiv 1sinsin)(

Domain:

Range:

11 x

1 2

sin

1sinsin,1when 1

yx

1 2

sin

1sinsin,1when 1

yx

xyiv 1sinsin)(

Domain:

Range:

11 x

1 2

sin

1sinsin,1when 1

yx

1 2

sin

1sinsin,1when 1

yx

0 0sin

0sinsin,0when 1

yx

11 y

xyiv 1sinsin)(

Domain:

Range:

11 x

1 2

sin

1sinsin,1when 1

yx

y

x

1

1-1-1

1 2

sin

1sinsin,1when 1

yx

0 0sin

0sinsin,0when 1

yx

11 y

xyiv 1sinsin)( xy 1sinsin Domain:

Range:

11 x

1 2

sin

1sinsin,1when 1

yx

y

x

1

1-1-1

1 2

sin

1sinsin,1when 1

yx

0 0sin

0sinsin,0when 1

yx

11 y

xyiv 1sinsin)( xy 1sinsin Domain:

Range:

11 x

1 2

sin

1sinsin,1when 1

yx

y

x

1

1-1-1

1 2

sin

1sinsin,1when 1

yx

0 0sin

0sinsin,0when 1

yx

11 y

Exercise 1C; 2 to 5ace,6a b i,iii, 9, 11 to 15