sinx + circle 90 o 180 o  0o0o 270 o 1 The Trigonometric Ratios for any angle 0 90 180 360270-90 -180 -270 -360 0 90180 270 -90 -180 -270 -360360 450.

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sinx + circle 90 o 180 o  0o0o 270 o 1 The Trigonometric Ratios for any angle o 0o0o 90 o 180 o 270 o 360 o -90 o -180 o -270 o -360 o -450 o 360 o 0o0o 90 o 180 o 270 o

ksinx x y = f(x) sinx 2sinx sinx y = ½sinx

Amplitude/Period x Sinx 2Sinx 3Sinx Amplitude  1 Period 360 o Amplitude  2 Period 360 o Amplitude  3 Period 360 o

kcosx x y = f(x) cosx ½cosx 2cosx 3cosx

ksinx x 4 x x x x y = sinx y = 2sinx y = 3sinx y = ½ sinx o 180 o 270 o 360 o -90 o -180 o -270 o -360 o o 180 o 270 o 360 o -90 o -180 o -270 o -360 o o 180 o 270 o 360 o -90 o -180 o -270 o -360 o o 180 o 270 o 360 o -90 o -180 o -270 o -360 o

x x x y = cosx y = 2cosx y = 3cosx y = ½ cosx o 180 o 270 o 360 o -90 o -180 o -270 o -360 o o 180 o 270 o 360 o -90 o -180 o -270 o -360 o o 180 o 270 o 360 o -90 o -180 o -270 o -360 o o 180 o 270 o 360 o -90 o -180 o -270 o -360 o x

x y = f(x) f(x) = sinx f(x) = sin2x f(x) = sin3x f(x) = sin ½ x

x y = f(x) f(x) = cosx f(x) = cos2x f(x) = cos3x f(x) = cos ½ x

sin kx x 4 xx x x y = sinx y = sin2x y = sin3x y = sin ½ x o 180 o 270 o 360 o -90 o -180 o -270 o -360 o o 180 o 270 o 360 o -90 o -180 o -270 o -360 o o 180 o 270 o 360 o -90 o -180 o -270 o -360 o o 180 o 270 o 360 o -90 o -180 o -270 o -360 o

cos kx x 4 x x x x y =cosx y = cos2x y = cos3x y = cos ½ x o 180 o 270 o 360 o -90 o -180 o -270 o -360 o o 180 o 270 o 360 o -90 o -180 o -270 o -360 o o 180 o 270 o 360 o -90 o -180 o -270 o -360 o o 180 o 270 o 360 o -90 o -180 o -270 o -360 o

tan x y = tan  0o0o 90 o 180 o 270 o 360 o -90 o -180 o -270 o -360 o 450 o -450 o x

y = sinx o 180 o 270 o 360 o -90 o -180 o -270 o -360 o o 180 o 270 o 360 o -90 o -180 o -270 o -360 o y = cosx y = tan  0o0o 90 o 180 o 270 o 360 o -90 o -180 o -270 o -360 o 450 o -450 o x x x

ksin x and kcos x y = sinx o 180 o 270 o 360 o -90 o -180 o -270 o -360 o o 180 o 270 o 360 o -90 o -180 o -270 o -360 o y = cosx y = 2sinx y = 2cosx x y = 3sinx o 180 o 270 o 360 o -90 o -180 o -270 o -360 o y = 3cosx x y = ½ sinx o 180 o 270 o 360 o -90 o -180 o -270 o -360 o y = ½ cosx x x

ksin x and -ksin x x x x x y = sinx y = -2sinx y = 3sinx y = ½ sinx o 180 o 270 o 360 o -90 o -180 o -270 o -360 o o 180 o 270 o 360 o -90 o -180 o -270 o -360 o o 180 o 270 o 360 o -90 o -180 o -270 o -360 o o 180 o 270 o 360 o -90 o -180 o -270 o -360 o y = - sinx y = 2sinx y = - 3sinx y = - ½ sinx

x x x y = cosx y = 2cosx y = 3cosx y = ½ cosx o 180 o 270 o 360 o -90 o -180 o -270 o -360 o o 180 o 270 o 360 o -90 o -180 o -270 o -360 o o 180 o 270 o 360 o -90 o -180 o -270 o -360 o o 180 o 270 o 360 o -90 o -180 o -270 o -360 o y = -cosx y = -2cosx y = -3cosx y = -½ cosx x

Grid x y = f(x)

Grid x o 180 o 270 o 360 o -90 o -180 o -270 o -360 o o 180 o 270 o 360 o -90 o -180 o -270 o -360 o x x x o 180 o 270 o 360 o -90 o -180 o -270 o -360 o o 180 o 270 o 360 o -90 o -180 o -270 o -360 o x