Graphs Flashcards
sin period
2π
cos period
2π
cos is sin shifted by…
π/2
sinusoidal function range
[-1, 1]
sin is symmetrical with respect to the…
origin
cos is symmetrical with respect to the…
y-axis
new period formula for transformed sinusoidal function
period = 2π/|B|
critical points are given by…
period/4
amplitude of tan is found at…
1/4 the period
tan period
π
tan vertical asymptotes
x = π/2 + πk
where K is any integer
new period formula for transformed tan
period = π/|B|
cot vertical asymptotes
x = π + πk
where k is any integer
—– and —- have a vertical asymptotes on the y-axis
cotangent
cosecant
sec period
2π
sec vertical asymptotes
x = π/2 + πk
where k is any integer
range of sec
(-∞,-1]U[1,∞)
new period formula for transformed sec
period = 2π/|B|
csc period
2π
csc vertical asymptotes
πk
where k is any integer
domain restriction to take inverse of sin
[-π/2, π/2]
domain restriction to take inverse of cos
[0, 1]
domain restriction to take inverse of tan
(-π/2, π/2)
interval for sin(sin-1x) = x
-1≤ x ≤ 1
interval for cos(cos-1x) = x
-1≤ x ≤ 1
interval for tan(tan-1x) = x
(-∞, ∞)
interval for sin-1(sinx) = x
-π/2 ≤ x ≤ π/2
interval for cos-1(cosx) = x
0 ≤ x ≤ π
interval for tan-1(tanx) = x
-π/2 < x < π/2
