Explanation:

The domain the the tangent role does not include any kind of values of x that are odd multiples of π/2 .

You are watching: The range of sine function is

The selection of the sine function is native <-1, 1>.

The period of the tangent role is π, vice versa, the period for both sine and also cosine is 2π.


Which of the complying with represents a sine wave v a selection of 

*
?


*


*


*


*


Explanation:

The selection of a sine wave is changed by the coefficient inserted in front of the basic equation. So, if friend have 

*
, this method that the highest suggest on the wave will be at 
*
 and the shortest at 
*
. However, if friend then begin to transition the equation vertically by including values, together in, 
*
, climate you must account for said shift. This would certainly make the minimum value to be 
*
 and the maximum worth to be 
*
. Because that our question, then, the is fine come use 
*
. The 
*
 for the duty parameter only transforms the period of the equation, do its waves "thinner."


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Example question #63 : Trigonometry


Which the the adhering to sine waves has actually a variety of 

*
 to 
*
?


Possible Answers:
Correct answer:

*


Explanation:

The variety of a sine wave is altered by the coefficient placed in prior of the basic equation. So, if friend have 

*
, this means that the highest suggest on the wave will certainly be at 
*
 and the shortest at 
*
; however, if friend then start to change the equation vertically by adding values, together in, 
*
, climate you should account for said shift. This would make the minimum worth to be 
*
 and the maximum worth to be 
*
.

For ours question, the variety of values covers 

*
. This variety is achieved by having either 
*
 or 
*
 as your coefficient. (
*
 merely flips the equation end the
*
-axis. The range "spread" remains the same.) We should make the top value to it is in
*
 instead of 
*
. To carry out this, you will must add 
*
 to 
*
. This requires an upward shift of 
*
. An instance of performing a shift like this is:

*

Among the possible answers, the one that functions is:

*

The

*
 parameter does no matter, together it only alters the frequency the the function.


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Example question #64 : Trigonometry


What is the variety of the trigonometric function given by the equation:

*


Possible Answers:
Correct answer:

*


Explanation:

The range of the sine and cosine features are the close up door interval indigenous the negative amplitude and also the confident amplitude. The amplitude is provided by the coefficient, 

*
 in the adhering to general equation: 
*
. For this reason we view the range is:
*


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Example question #65 : Trigonometry


What is the variety of the complying with trigonometric equation:

*
?


Possible Answers:
Correct answer:

*


Explanation:

The selection of a sine or cosine duty spans indigenous the negative amplitude come the positive amplitude. The amplitude is 

*
 in the basic formula: 
*
Thus we see amplitude that our role is 
*
 and so the selection is:

*


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