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Discuss what you believe to be the domain which will make y= arcos(x) and y =...

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foxwit | Student, Undergraduate | (Level 1) Salutatorian

Posted July 24, 2013 at 5:39 PM via web

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Discuss what you believe to be the domain which will make y= arcos(x) and y = arctan(x), functions.

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aruv | High School Teacher | (Level 2) Valedictorian

Posted July 24, 2013 at 7:15 PM (Answer #1)

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`y=cos^(-1)(x)`    (i)

since

`x=cos(y)`  is one to one  and onto if `y in[0,pi]` .

Thus (i) is function if `x in[-1,1] and yin[0,pi]`

`y=tan^(-1)(x)`     (ii)

since

`x=tan (y)`   is one to one and onto if `yin(-pi/2,pi/2)`

Thus (ii) is function if `x in (-oo,oo) and yin(-pi/2,pi/2)`

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