Parent Trig Graphswith translations

By: Jeffrey Bivin

Lake Zurich High School

jeff.bivin@lz95.org

Last Updated: October 11, 2005

Jeff Bivin -- LZHS

y = sin(2x)

Jeff Bivin -- LZHS

y = sin(2x)

Jeff Bivin -- LZHS

y = sin(2x)Amplitude = 1

Period = π

Phase shift = 0

Jeff Bivin -- LZHS

y = 3sin(x)

Jeff Bivin -- LZHS

y = 3sin(x)Amplitude = 3

Period = 2π

Phase shift = 0

Jeff Bivin -- LZHS

y = -4sin(2x)

Jeff Bivin -- LZHS

y = -4sin(2x)

Jeff Bivin -- LZHS

y = -4sin(2x)

Amplitude = 4

Period = π

Phase shift = 0

Jeff Bivin -- LZHS

y = sin(x + π/2) x + π/2 = 0

x = -π/2

π/2

Jeff Bivin -- LZHS

y = sin(x + π/2) x + π/2 = 0

x = -π/2

π/2

Amplitude = 1

Period = 2π

Phase shift = -π/2

Jeff Bivin -- LZHS

xxf2

1cos)(

Jeff Bivin -- LZHS

xxf2

1cos)(

Amplitude = 1

Period = 4π

Phase shift = 0

Jeff Bivin -- LZHS

xxf 2cos)(

Jeff Bivin -- LZHS

xxf 2cos)(

Amplitude = 1

Period = π

Phase shift = 0

Jeff Bivin -- LZHS

xxf 2cos3)(

Jeff Bivin -- LZHS

Amplitude = 3

Period = π

Phase shift = 0

xxf 2cos3)(

Jeff Bivin -- LZHS

3cos2)(

xxf 0

3

x

3

x

π/3

Jeff Bivin -- LZHS

Amplitude = 2

Period = 2π

Phase shift = π/3

03

x

3

x

3cos2)(

xxf

π/3

Jeff Bivin -- LZHS

12cos3)( xxf 02 x

2

x

π/2

Jeff Bivin -- LZHS

12cos3)( xxf

UP1

UP1

Jeff Bivin -- LZHS

12cos3)( xxf

UP1

UP1

Amplitude = 3

Period = π

Phase shift = π/2

Jeff Bivin -- LZHS

Jeff Bivin -- LZHS

y = csc(x)

)sin(

1

xy

Jeff Bivin -- LZHS

y = csc(x)

Amplitude = 1

Period = 2π

Phase shift = 0

)sin(

1

xy

Jeff Bivin -- LZHS

y = sec(x)

)cos(

1

xy

Jeff Bivin -- LZHS

y = sec(x)

Amplitude = 1

Period = 2π

Phase shift = 0

)cos(

1

xy

Jeff Bivin -- LZHS

y = 3sec(x-π) 0 x

x

π

Jeff Bivin -- LZHS

y = 3sec(x-π) 0 x

x

π

Amplitude = 3

Period = 2π

Phase shift = π

Jeff Bivin -- LZHS

Jeff Bivin -- LZHS

y = tan(x)

)cos(

)sin(

x

xy

Jeff Bivin -- LZHS

y = tan(x)

Amplitude = 1

Period = π

Phase shift = 0

Jeff Bivin -- LZHS

y = cot(x)

)sin(

)cos(

x

xy

Jeff Bivin -- LZHS

y = cot(x)

Amplitude = 1

Period = π

Phase shift = 0

Jeff Bivin -- LZHS

y = tan(2x+π)

)2cos(

)2sin(

x

xy

02 x

2

x

π/2

Jeff Bivin -- LZHS

y = tan(2x+π) 02 x

2

x

π/2

Jeff Bivin -- LZHS

y = tan(2x+π) 02 x

2

x

π/2

Amplitude = 1

Period = π/2

Phase shift = - π/2

Jeff Bivin -- LZHS

Jeff Bivin -- LZHS