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Parent Trig Graphs

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Parent Trig Graphs

with translations

By: Jeffrey Bivin

Lake Zurich High School

jeff.bivin@lz95.org

Last Updated: October 11, 2005

sine

and

cosine

functions

Jeff Bivin -- LZHS

squeeze

squeeze

Jeff Bivin -- LZHS

Jeff Bivin -- LZHS

Amplitude = 1

Period = π

Phase shift = 0

Jeff Bivin -- LZHS

stretch

stretch

Jeff Bivin -- LZHS

Amplitude = 3

Period = 2π

Phase shift = 0

Jeff Bivin -- LZHS

flip

stretch

squeeze

stretch

flip

squeeze

Jeff Bivin -- LZHS

Jeff Bivin -- LZHS

Amplitude = 4

Period = π

Phase shift = 0

Jeff Bivin -- LZHS

π/2

x + π/2 = 0

x = -π/2

Jeff Bivin -- LZHS

π/2

x + π/2 = 0

x = -π/2

Amplitude = 1

Period = 2π

Phase shift = -π/2

Jeff Bivin -- LZHS

stretch

Jeff Bivin -- LZHS

Amplitude = 1

Period = 4π

Phase shift = 0

Jeff Bivin -- LZHS

squeeze

squeeze

Jeff Bivin -- LZHS

Amplitude = 1

Period = π

Phase shift = 0

Jeff Bivin -- LZHS

stretch

squeeze

stretch

squeeze

Jeff Bivin -- LZHS

Amplitude = 3

Period = π

Phase shift = 0

Jeff Bivin -- LZHS

stretch

stretch

π/3

Jeff Bivin -- LZHS

π/3

Amplitude = 2

Period = 2π

Phase shift = π/3

Jeff Bivin -- LZHS

stretch

squeeze

stretch

squeeze

π/2

Jeff Bivin -- LZHS

UP1

UP1

Jeff Bivin -- LZHS

Amplitude = 3

Period = π

Phase shift = π/2

UP1

UP1

Jeff Bivin -- LZHS

secant

and

cosecant

functions

Jeff Bivin -- LZHS

Jeff Bivin -- LZHS

Amplitude = 1

Period = 2π

Phase shift = 0

Jeff Bivin -- LZHS

y = cos(x)

Jeff Bivin -- LZHS

Amplitude = 1

Period = 2π

Phase shift = 0

Jeff Bivin -- LZHS

stretch

stretch

π

Jeff Bivin -- LZHS

π

Amplitude = 3

Period = 2π

Phase shift = π

Jeff Bivin -- LZHS

tangent

and

cotangent

functions

Jeff Bivin -- LZHS

y = cos(x)

Jeff Bivin -- LZHS

Amplitude = 1

Period = π

Phase shift = 0

Jeff Bivin -- LZHS

y = sin(x)

Jeff Bivin -- LZHS

Amplitude = 1

Period = π

Phase shift = 0

Jeff Bivin -- LZHS

squeeze

squeeze

π/2

y = cos(x)

Jeff Bivin -- LZHS

π/2

Jeff Bivin -- LZHS

π/2

Amplitude = 1

Period = π/2

Phase shift = - π/2

Jeff Bivin -- LZHS

THAT'S

ALL

FOLKS

Jeff Bivin -- LZHS