Graphing trig

39
Parent Trig Graphs with translations

Transcript of Graphing trig

1π 2π

1

−1

Parent Trig Graphs

with translations

1π 2π

1

−1

1π 2π

1

−1

y = sin(2x)

1π 2π

1

−1

y = sin(2x)

1π 2π

1

−1

y = sin(2x)Amplitude = 1

Period = π

Phase shift = 0

1π 2π

1

−1

y = 3sin(x)

1π 2π

1

−1

y = 3sin(x)Amplitude = 3

Period = 2π

Phase shift = 0

1π 2π

1

−1

y = -4sin(2x)

1π 2π

1

−1

y = -4sin(2x)

Jeff Bivin -- LZHS

1π 2π

1

−1

y = -4sin(2x)

Amplitude = 4

Period = π

Phase shift = 0

1π 2π

1

−1

y = sin(x + π/2)

x + π/2 = 0x = -π/2

π/2

1π 2π

1

−1

y = sin(x + π/2)

x + π/2 = 0x = -π/2

π/2

Amplitude = 1

Period = 2π

Phase shift = -π/2

1π 2π

1

−1

= xxf2

1cos)(

1π 2π

1

−1

= xxf2

1cos)(

Amplitude = 1

Period = 4π

Phase shift = 0

1π 2π

1

−1

( )xxf 2cos)( =

1π 2π

1

−1

( )xxf 2cos)( =

Amplitude = 1

Period = π

Phase shift = 0

1π 2π

1

−1

( )xxf 2cos3)( =

1π 2π

1

−1

Amplitude = 3

Period = π

Phase shift = 0

( )xxf 2cos3)( =

1π 2π

1

−1

−=

3cos2)(

πxxf 0

3=− π

x

3

π=x

π/3

1π 2π

1

−1

Amplitude = 2

Period = 2π

Phase shift = π/3

03

=− πx

3

π=x

−=

3cos2)(

πxxf

π/3

1π 2π

1

−1

( ) 12cos3)( +−= πxxf 02 =− πx

2

π=x

π/2

1π 2π

1

−1

( ) 12cos3)( +−= πxxf

UP1

UP1

1π 2π

1

−1

( ) 12cos3)( +−= πxxf

UP1

UP1

Amplitude = 3

Period = π

Phase shift = π/2

1π 2π

1

−1

1π 2π

1

−1

y = csc(x)

)sin(

1

xy =

1π 2π

1

−1

y = csc(x)

Amplitude = 1

Period = 2π

Phase shift = 0

)sin(

1

xy =

Jeff Bivin -- LZHS

1π 2π

1

−1

y = sec(x)

)cos(

1

xy =

1π 2π

1

−1

y = sec(x)

Amplitude = 1

Period = 2π

Phase shift = 0

)cos(

1

xy =

1π 2π

1

−1

y = 3sec(x-π)

0=− πx

π=x

π

1π 2π

1

−1

y = 3sec(x-π)

0=− πx

π=x

π

Amplitude = 3

Period = 2π

Phase shift = π

1π 2π

1

−1

1π 2π

1

−1

y = tan(x)

)cos(

)sin(

x

xy =

Jeff Bivin -- LZHS

1π 2π

1

−1

y = tan(x)

Amplitude = 1

Period = π

Phase shift = 0

1π 2π

1

−1

y = cot(x)

)sin(

)cos(

x

xy =

1π 2π

1

−1

y = cot(x)

Amplitude = 1

Period = π

Phase shift = 0

1π 2π

1

−1

y = tan(2x+π)

)2cos(

)2sin(

ππ

++=x

xy

02 =+ πx

2

π−=x

π/2

Jeff Bivin -- LZHS

1π 2π

1

−1

y = tan(2x+π)

02 =+ πx

2

π−=x

π/2

1π 2π

1

−1

y = tan(2x+π)

02 =+ πx

2

π−=x

π/2

Amplitude = 1

Period = π/2

Phase shift = - π/2

1π 2π

1

−1