1)
a) y = sin x
Domain: All real numbers
Range: [-1, 1]
Period: 2π
x-ints: x = nπ, n integer
y-int: (0, 0)
b) y = cos x
Domain: All real numbers
Range: [-1, 1]
Period: 2π
x-ints: x = π/2 + nπ, n integer
y-int: (0, 1)
c) y = tan x
Domain: x ≠ π/2 + nπ, n integer
Range: All real numbers
Period: π
x-ints: x = nπ, n integer
y-int: (0, 0)
d) y = cot x
Domain: x ≠ nπ, n integer
Range: All real numbers
Period: π
x-ints: x = π/2 + nπ, n integer
y-int: None (undefined at x=0)
2)
a) y = 4sinx
Amplitude: 4
Period: 2π
Phase shift: 0
Vertical displacement: 0
Reflected? No
b) y = -3cosx
Amplitude: 3
Period: 2π
Phase shift: 0
Vertical displacement: 0
Reflected? Yes (over x-axis)
c) y = 3 - ½ sin(¼(x - 3))
Amplitude: ½
Period: 8π
Phase shift: 3 right
Vertical displacement: 3 up
Reflected? No
d) y = cos(π/6 x) + 4
Amplitude: 1
Period: 12
Phase shift: 0
Vertical displacement: 4 up
Reflected? No
e) y = 3cos(2x - π) + 1
Amplitude: 3
Period: π
Phase shift: π/2 right
Vertical displacement: 1 up
Reflected? No
f) y = -sin3x
Amplitude: 1
Period: 2π/3
Phase shift: 0
Vertical displacement: 0
Reflected? Yes (over x-axis)
Parent Tip: Review the logic above to help your child master the concept of trigonometric graph worksheet.
