Graphs of Trigonometric Functions Flashcards
A sine graph looks like:
A mountain and a valley.
A cosine graph looks like:
A raven.
y=d+asinb(x-c/b)
y=d+acosb(x-c/b)
y=d+acscb(x-c/b)
y=d+asecb(x-c/b)
Period…
2π/b
Time to repeat a cycle.
y=d+asinb(x-c/b)
y=d+acosb(x-c/b)
y=d+acscb(x-c/b)
y=d+asecb(x-c/b)
y=d+atanb(x-c/b)
y=d+acotb(x-c/b)
Amplitude…
|a|
Affects the height of the function (y-axis).
y=d+asinb(x-c/b)
y=d+acosb(x-c/b)
y=d+acscb(x-c/b)
y=d+asecb(x-c/b)
y=d+atanb(x-c/b)
y=d+acotb(x-c/b)
Vertical shift (V.S.)…
d=amp+min.
Shift on the y-axis.
y=d+asinb(x-c/b)
y=d+acosb(x-c/b)
y=d+acscb(x-c/b)
y=d+asecb(x-c/b)
y=d+atanb(x-c/b)
y=d+acotb(x-c/b)
Phase shift (P.S.)…
c/b
Shift across the x-axis.
What order is recommended for graphing points after a transformation of a cosine graph?
Left, right, middle, last.
y=tanx
Asymptotes…
x = π/2 + πn
y=tanx
Period…
π
y=cotx
Asymptotes…
x = π + πn
y=cotx
Period…
π
y=cscx
Asymptotes…
x = nπ
y=cscx
Period…
2π
y=cscx
Domain…
all reals, x ≠ nπ
y=cscx
Range…
(-∞, -1] U [1, ∞)
