1π 2π
1
−1
Parent Trig Graphs
with translations
y = sin(2x)
y = sin(2x)Amplitude = 1
Period = π
Phase shift = 0
y = 3sin(x)
y = 3sin(x)Amplitude = 3
Period = 2π
y = -4sin(2x)
Jeff Bivin -- LZHS
Amplitude = 4
y = sin(x + π/2)
x + π/2 = 0x = -π/2
π/2
Amplitude = 1
Phase shift = -π/2
= xxf2
1cos)(
Period = 4π
( )xxf 2cos)( =
( )xxf 2cos3)( =
Amplitude = 3
−=
3cos2)(
πxxf 0
3=− π
x
3
π=x
π/3
Amplitude = 2
Phase shift = π/3
03
=− πx
πxxf
( ) 12cos3)( +−= πxxf 02 =− πx
2
( ) 12cos3)( +−= πxxf
UP1
Phase shift = π/2
y = csc(x)
)sin(
xy =
y = sec(x)
)cos(
y = 3sec(x-π)
0=− πx
π
Phase shift = π
y = tan(x)
y = cot(x)
y = tan(2x+π)
)2cos(
)2sin(
ππ
++=x
xy
02 =+ πx
π−=x
Period = π/2
Phase shift = - π/2
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