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 | 24th Apr, 2014, 11:03: PM

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  | 25th Apr, 2014, 10:11: AM

Queries asked on Sunday & after 7pm from Monday to Saturday will be answered after 12pm the next working day.