O TRIGONOMETRIC FUNCTIONSDomains and ranges of trigonometric functionsWhat are the domains and ranges of the following functions?Function(Choose one)DomainyCOSxTCRangeThe set of all real numbers, except odd integer multiples of2DomainThe set of all real numbers from -1 to 1y=tanxThe set of all real numbers, except integer multiples of tRangeThe set of all real numbers less than or equal to -1 or greater than or equal to 1The set of all real numbersDomainy=CSCX(Choose one)Range?X

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Asked Sep 26, 2019
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O TRIGONOMETRIC FUNCTIONS
Domains and ranges of trigonometric functions
What are the domains and ranges of the following functions?
Function
(Choose one)
Domain
yCOSx
TC
Range
The set of all real numbers, except odd integer multiples of
2
Domain
The set of all real numbers from -1 to 1
y=tanx
The set of all real numbers, except integer multiples of t
Range
The set of all real numbers less than or equal to -1 or greater than or equal to 1
The set of all real numbers
Domain
y=CSCX
(Choose one)
Range
?
X
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O TRIGONOMETRIC FUNCTIONS Domains and ranges of trigonometric functions What are the domains and ranges of the following functions? Function (Choose one) Domain yCOSx TC Range The set of all real numbers, except odd integer multiples of 2 Domain The set of all real numbers from -1 to 1 y=tanx The set of all real numbers, except integer multiples of t Range The set of all real numbers less than or equal to -1 or greater than or equal to 1 The set of all real numbers Domain y=CSCX (Choose one) Range ? X

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Expert Answer

Step 1

Given trigonometric functions we have to find the domain and range of the functions.

Step 2

a) y= cos x

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Domain: Since y is defined for any x with y = cos x, there is no domain restrictions Thus, domain of cos x is the set of all real numbers. Range The x - coordinate is minimum at (-1,0) i.e. -1 and the maximum at (1,0) i.e. 1. Thus, the range of the function is [-1, ]

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Step 3

b) y = tan...

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Since tan x = and we know the tan x will be undefined for cos x = 0. So, we eliminate COS X TT = 0 2 all the chances of x for which cos x will be 0. For instance, cos Thus, tan x is undefined when x is odd integer multiples of TT Domain of tan x is set of all real values, except odd integer multiples of Range sinx can be any number, range is (-o, oo) Since COS X

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