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Graphing sine and cosine functions
y = asin(b(x-c)) + d OR y = acos(b(x-c)) + d
General equation of a trigonometric function
amplitude
the absolute value of a
(max-min)/2
how to find the amplitude
period
the horizontal distance between two maximum or two minimums OR two times the horizontal distance between a maximum and a minimum
period = (2π)/b
how to find the period
find any point on the principal axis where the curve goes up after
how to find the phase shift, c, for a sine graph
find any maximum point
how to find the phase shift, c, for a cosine graph
a
affects vertical stretch
b > 0
affects horizontal stretch
c
affects horizontal translation
d
affects vertical translation
y = d
principal axis
(max + min)/2
how to find the principal axis
(0,0), (π/2, 1), (π, 0), (3π/2, -1), (2π, 0)
5 major points of a sine parent graph
(0, 1), (π/2, 0), (π, -1), (3π/2, 0), (2π, 1)
5 major points of a cosine graph
the number of periods
Iterations in SinReg 1
how long does it take to complete one cycle (time)
Period in SinReg 1
What does a sine graph look like?
the sine graph begins at the principal axis
What does a cosine graph look like?
the cosine graph begins at a maximum
Equation of a tangent function
y = atan(b(x - c)) + d
a = vertical dilation
period = π/b
c > 0 shifts the graph to the right
c < 0 shifts the graph to the left
y = d: principal axis
Note
Flashcard