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sine cosine graphs: period and maximums
Поширений: Smith
-7
-6
-5
The PERIOD of a function is how long it takes
(how far it travels ←horizontally→)
before the pattern repeats itself.

The period of the function above is 2
-4
-3
-2
-1
1
Period = 2
2
3
4
5
6
7
-7
-6
the period of this function is :             units
-5
-4
-3
-2
-1
Period
1
2
3
4
5
6
7
-7
-6
-5
           Period =           units
-4
-3
-2
-1
1
2
3
4
5
6
7
-7
-6
3 units
-5
           Period =   3      units
-4
-3
-2
-1
1
2
3
4
5
6
7
2
-2
4
-4
6
-6
π
-2π
-3π
The period of this cosine function is 2π
It repeats every 2π units
2
-2
4
-4
π
-2π
-7

This graph is in RADIANS

This is the function

f(x) = sin x

-6

Notice how π (3.14)

is listed right after 3

-5
-4
-3
-2
-1
1
2
2
Period is:
3
π
4
5
6
7
-7
-6
Zeroes occur at  ...-4, 0, 4...
Zeroes of this function occur where the
graph hits the x-axis (where y=0)
-5
-4
-3
-2
-1
1
2
3
4
5
6
7
-7
-6
Where is the zero in the interval [1,5] ?
Zeroes of this function occur where the
graph hits the x-axis (where y=0)
-5
-4
-3
-2
-1
1
[
2
Interval
3
4
x=
]
5
6
7
-7
[
Where is the zero in the interval [-7,-3] ?
-6
Interval
Zeroes of this function occur where the
graph hits the x-axis (where y=0)
-5
-4
-3
]
-2
-1
1
2
3
4
x=
5
6
7
-7
Where is the zero in the interval [-1,3] ?
-6
Zeroes of this function occur where the
graph hits the x-axis (where y=0)
-5
-4
-3
-2
-1
[
Interval
1
2
]
3
4
x=
5
6
7
-7
-6
The maximum value of this function is y=
The maximum value of the function
is where y is at its ↑ highest ↑ point
-5
-4
-3
-2
-1
1
2
4
3
1
2
3
4
5
6
7
-7
-6
           Maximum y =    
-5
-4
-3
-2
-1
1
2
3
4
5
6
7
-7
-6
The maximum value in the interval [-4,-2] is
 
-5
-4
[
Interval
-3
-2
]
y=
-1
1
2
4
3
1
2
3
4
5
6
7
2
-2
4
-4
π
-2π
-7
-6
-5
Period of this function:
-4
-3
-2
-1
1
π
4
2
3
4
5
6
7
2
-2
4
-4
π
-2π
-7
-6
-5
Approximate zero of
this function in the
interval [0,4]
-4
-3
-2
-1
1
1.57
1.95
2.23
2
3
4
5
6
7
2
-2
4
-4
π
-2π
-7
-6
-5
Approximate maximum
 of this function in the
interval [1,4] is y=
-4
-3
-2
-1
1
-.5
.54
 1
2
3
4
5
6
7
2
-2
4
-4
π
-2π
-7
y=1 is the overall maximum,
but it occurs when x=0,
outside the[1,4] interval
-6
-5
Approximate maximum
 of this function in the
interval [1,4]
-4
-3
-2
-1
[
1
y=
This
interval
only
2
3
.54
]
4
5
6
7
The end  (this is the graph of the secant function)
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