Transcript graphs of trigonometry functions

and their inverses
Nate Long
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 Period
 Units
 Amplitude
 Phase Shift
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 The length it takes the graph to complete 1
full cycle
Period= 4
One Full Cycle of the
Sine Graph
Period= 2p
One Full Cycle of the
Cosine Graph
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 Used to divide the period up into equal parts
so the graph is even
The units are 90
Period= 360
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 The distance from the middle of the graph to
the top and from the middle of the graph to
the bottom
Use these numbers to
find the amplitude
1 Unit
1 Unit
Amplitude= 1
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 The amount a graph moves right or left
Red line is the original graph, blue line is the shifted graph
Phase Shift= p/6
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y= A cos (Bx+C)
y=A sin
(Bx+C)
 Period= 2p/B
 Units= P/4
 Amplitude= |A|
 Phase Shift= - C/B
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 All trigonometric graphs must be functions
 Use the vertical line test to see if the graph is a
function- if a vertical line is drawn, it can intersect
the graph at only 1 point
Sine
Graph
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Sine
Inverse
Graph
 This is an example of a
sine inverse graph, but
notice that this is not a
function, because it
fails the vertical line
test.
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 To solve this, we can
only show the portion
of the graph that is a
function
Now our graph passes the
vertical line test
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Dotted lines show where graph would continue, but
can’t because it would violate the Vertical Line Test
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 In a cosine function, the range is 0≤x≤π (The
area between 0 and π on a graph is
Quadrants 1 and 2)
 In a sine function, the range is - π/2≤x≤π/2
(This area is Q4 and Q1)
 Period= 2p/B
 Units= P/4
 Amplitude= |A|
 Phase Shift= - C/B
 All Graphs Must
Be Functions
 An inverse graph
is has the same
shape as it’s
original graph, but
only the part that
is a function is
shown/drawn