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Parent Trig Graphs. with translations By: Jeffrey Bivin Lake Zurich High School [email protected] Last Updated: October 11, 2005. sine and cosine. functions. Jeff Bivin -- LZHS. squeeze. squeeze. y = sin(2x). Jeff Bivin -- LZHS. y = sin(2x). Jeff Bivin -- LZHS.

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Parent trig graphs

Parent Trig Graphs

with translations

By: Jeffrey Bivin

Lake Zurich High School

[email protected]

Last Updated: October 11, 2005


sine

and

cosine

functions

Jeff Bivin -- LZHS


Y sin 2x

squeeze

squeeze

y = sin(2x)

Jeff Bivin -- LZHS


Y sin 2x1
y = sin(2x)

Jeff Bivin -- LZHS


Y sin 2x2
y = sin(2x)

Amplitude = 1

Period = π

Phase shift = 0

Jeff Bivin -- LZHS


Y 3sin x

stretch

stretch

y = 3sin(x)

Jeff Bivin -- LZHS


Y 3sin x1
y = 3sin(x)

Amplitude = 3

Period = 2π

Phase shift = 0

Jeff Bivin -- LZHS


Y 4sin 2x

flip

stretch

squeeze

stretch

flip

squeeze

y = -4sin(2x)

Jeff Bivin -- LZHS


Y 4sin 2x1
y = -4sin(2x)

Jeff Bivin -- LZHS


Y 4sin 2x2
y = -4sin(2x)

Amplitude = 4

Period = π

Phase shift = 0

Jeff Bivin -- LZHS


Y sin x 2

π/2

y = sin(x + π/2)

x + π/2 = 0

x = -π/2

Jeff Bivin -- LZHS


Y sin x 21

π/2

y = sin(x + 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


Y csc x
y = csc(x)

Jeff Bivin -- LZHS


Y csc x1
y = csc(x)

Amplitude = 1

Period = 2π

Phase shift = 0

Jeff Bivin -- LZHS


Y sec x
y = sec(x)

y = cos(x)

Jeff Bivin -- LZHS


Y sec x1
y = sec(x)

Amplitude = 1

Period = 2π

Phase shift = 0

Jeff Bivin -- LZHS


Y 3sec x

stretch

stretch

y = 3sec(x-π)

π

Jeff Bivin -- LZHS


Y 3sec x1
y = 3sec(x-π)

π

Amplitude = 3

Period = 2π

Phase shift = π

Jeff Bivin -- LZHS


tangent

and

cotangent

functions

Jeff Bivin -- LZHS


Y tan x
y = tan(x)

y = cos(x)

Jeff Bivin -- LZHS


Y tan x1
y = tan(x)

Amplitude = 1

Period = π

Phase shift = 0

Jeff Bivin -- LZHS


Y cot x
y = cot(x)

y = sin(x)

Jeff Bivin -- LZHS


Y cot x1
y = cot(x)

Amplitude = 1

Period = π

Phase shift = 0

Jeff Bivin -- LZHS


Y tan 2x

squeeze

squeeze

y = tan(2x+π)

π/2

y = cos(x)

Jeff Bivin -- LZHS


Y tan 2x1
y = tan(2x+π)

π/2

Jeff Bivin -- LZHS


Y tan 2x2
y = tan(2x+π)

π/2

Amplitude = 1

Period = π/2

Phase shift = - π/2

Jeff Bivin -- LZHS


THAT'S

ALL

FOLKS

Jeff Bivin -- LZHS


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