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CBSE Class 12-science Answered

Kindly help me understand the concept of Range . I find it difficult to determine ranges of trigonometric functions .. for e.g 4tanx cos x 

Asked by Rucha Madke | 24 Apr, 2014, 11:03: PM
answered-by-expert Expert Answer
Let y=f(x)
 
Here x is the independent variable and y is the dependent variable.
 
The set of values that x can take is the domain of the function.
 
The set of values that y can take is the range of the function.
 
Now consider the given function,
 
y equals f open parentheses x close parentheses equals 4 tan open parentheses x close parentheses cos open parentheses x close parentheses R e w r i t e space t h e space a b o v e space f u n c t i o n space a s y equals 4 cross times fraction numerator sin open parentheses x close parentheses over denominator cos open parentheses x close parentheses end fraction cross times cos open parentheses x close parentheses rightwards double arrow y equals 4 sin open parentheses x close parentheses T h e space d o m a i n space o f space t h e space f u n c t i o n space sin open parentheses x close parentheses space i s space R comma space t h a t space i s space f r o m space minus infinity space t o space plus infinity. T h e space r a n g e space o f space t h e space f u n c t i o n space sin open parentheses x close parentheses space i s space f r o m space minus 1 space t o space 1 T h u s space t h e space r a n g e space o f space t h e space f u n c t i o n space y equals 4 sin open parentheses x close parentheses space i s space f r o m space minus 4 space t o space 4 comma space t h a t space i s space minus 4 less or equal than f open parentheses x close parentheses less or equal than 4.
 
Let us observe the following graph:
 
We can easily observe that the range of the given function varies from -4 to 4 for all values of x.
 
Answered by | 25 Apr, 2014, 10:11: AM

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