The function is periodic meaning that it repeats the pattern shown for both positive and negative x The domain shown constitutes one cycle of the periodic function and the period on an angular basis is 2 ID: 790193
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Slide1
Properties of Sine Function
Slide2The function is
periodic
, meaning that it repeats the pattern shown for both positive and negative
x
. The domain shown constitutes
one cycle
of the periodic function and the
period
on an angular basis is 2
radians.
The sine function is an odd function.
Slide3A. Graph
Slide4Domain:
all real numbers
Range:
[-1 , 1]
Period =
2pi
X intercepts:
x = k pi , where k is an integer.
Y intercepts:
y = 0
Maximum points:
(pi/2 + 2 k pi , 1) , where k is an integer.
Slide5Maximum points:
(pi/2 + 2 k pi , 1) , where k is an integer.
Minimum points:
(3pi/2 + 2 k pi , -1) , where k is an integer.
Symmetry:
since sin(-x) = - sin (x) then sin (x) is an odd function and its graph is symmetric with respect to the
origon
(0 , 0).
Slide6Intervals of Increase/Decrease:
over one period and from 0 to 2pi, sin (x) is increasing on the intervals (0 , pi/2) and (3pi/2 , 2pi), and decreasing on the interval (pi/2 , 3pi/2).
Slide7Source
http://www.analyzemath.com/trigonometry/properties.html