Trigonometric Graph Information

y=sin x

y=cos x

y=tan x

y=cot x

y=sec x

y=csc x

y=sin x y=cos x y=tan x y=cot x y=csc x y=sec x

y = aTRIG(bx + c) + d Amplitude (sine/cosine only) – (a) how high/low graph goes Period how far left/right graph goes Vertical Shift – (d) how far graph moves up/down Horizontal Shift – how far graph moves left/right

y = aTRIG(bx + c) + d a = b = c = d = Amplitude: a Vertical Shift: d Period: Horizontal Shift: y = 3sin(4x + 5) + 6 a = 3 b = 4 c = 5 d = 6 Amplitude: 3 Vertical Shift: 6 up Period: Horizontal Shift:

Amplitude: 2 Vertical Shift: 1 down Period: Horizontal Shift: y = 2cos(2x + ) - 1 a = 2 b = 2 c = d = -1 Amplitude: None Vertical Shift: 2 down Period: Horizontal Shift: y = sec(3x - ) - 2 a = 1 b = 3 c = d = -2

Amplitude: None Vertical Shift: 2 up Period: Horizontal Shift: y = 3tan(x + ) + 2 a = 3 b = 1 c = d = 2 Amplitude: 2 Vertical Shift: 1 down Period: Horizontal Shift: y = 2cos(4x - ) - 1 a = 2 b = 4 c = d = -1

Equation Amplitude Vertical Shift Period Horizontal Shift 2 1 up 2 flip 2 down None 1 down None 4 down None 3 down None

Equation Amplitude Vertical Shift Period Horizontal Shift None 1 down 2 flip 1 up None 3 up 1 flip 1 down None 0 1 up

Equation Amplitude Vertical Shift Period Horizontal Shift None 2 up 4 flip None 2 up 2 flip 1 up None 1 down None 1 up