#A = "Amplitude"##2pi//B = "Period"##-C//B = "Phase shift"##D = "Vertical shift"#

The maximum domain the a function is provided by all the worths in which the is fine defined:

#"Domain" = x in RR and also f(x) " is defined"#

Since the sine role is characterized everywhere top top the real numbers, its set is #RR#.

You are watching: What is the range of a sine function

As #f# is a regular function, its variety is a bounded interval given by the max and min worths of the function. The maximum output of #sinx# is #1#, while its minimum is #-1#.

Hence:

#"Range" = or "Range" = #

The selection depends on the authorize of #A#. However, if we allow that

# = #

then the range is much more simply identified as .

As a conclusion,

#f:RR -> #


Answer attach
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Sridhar V.
Jul 26, 2018

#" "#Domain:

#color(blue)((-oo

Interval Notation: #color(green)((-oo, oo)#

Range:

#color(blue)((-1

Interval Notation: #color(green)(<-1, 1>#


Explanation:

#" "#Domain and range of a SIN Graph:

Let united state look in ~ the SIN Graph first:

*

#color(blue)("Domain :"#

The domain of a duty is the set of entry values for which the duty is real and also defined.

#color(blue)((-oo

Domain restriction provided for the SIN Graph to display screen ONE complete cycle.

#color(blue)("Range :"#

The collection of output worths (of the dependency variable) for which the role is defined.

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As you can conveniently observe, the SIN graph go up until #color(blue)(1# and also goes down until #color(blue)(-1#

#color(blue)((-1

Hope this helps.


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