Lake Zurich High School 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

y = sin(2x) squeeze squeeze 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) stretch stretch Jeff Bivin -- LZHS

y = 3sin(x) Amplitude = 3 Period = 2π Phase shift = 0 Jeff Bivin -- LZHS

y = -4sin(2x) flip stretch squeeze squeeze 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

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 squeeze Jeff Bivin -- LZHS

Amplitude = 3 Period = π Phase shift = 0 Jeff Bivin -- LZHS

π/3 stretch Jeff Bivin -- LZHS

π/3 Amplitude = 2 Period = 2π Phase shift = π/3 Jeff Bivin -- LZHS

π/2 stretch squeeze squeeze Jeff Bivin -- LZHS

UP 1 UP 1 Jeff Bivin -- LZHS

UP 1 UP 1 Amplitude = 3 Period = π Phase shift = π/2 Jeff Bivin -- LZHS

secant and cosecant functions Jeff Bivin -- LZHS

y = csc(x) Jeff Bivin -- LZHS

y = csc(x) Amplitude = 1 Period = 2π Phase shift = 0 Jeff Bivin -- LZHS

y = sec(x) y = cos(x) Jeff Bivin -- LZHS

y = sec(x) Amplitude = 1 Period = 2π Phase shift = 0 Jeff Bivin -- LZHS

y = 3sec(x-π) π stretch Jeff Bivin -- LZHS

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 = cos(x) Jeff Bivin -- LZHS

y = tan(x) Amplitude = 1 Period = π Phase shift = 0 Jeff Bivin -- LZHS

y = cot(x) y = sin(x) Jeff Bivin -- LZHS

y = cot(x) Amplitude = 1 Period = π Phase shift = 0 Jeff Bivin -- LZHS

y = tan(2x+π) π/2 y = cos(x) squeeze squeeze Jeff Bivin -- LZHS

y = tan(2x+π) π/2 Jeff Bivin -- LZHS

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