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What is the domain of y=tan1 / 2   θ ?
a. all real numbers
d. all real numbers except nπ , where n is an odd integer.

 Jan 17, 2019
 #1
avatar+23494 
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Tan = sin / cos      we cannot have cos = 0   (denominator cannot = 0)

      cos = 0 at  odd multiples of pi/2      1/2 theta cannot equal on odd  multiple of pi/2

 

So  all theta not equal to odd numbers of pi     ( pi  3 pi     5 pi etc )

 Jan 17, 2019
edited by ElectricPavlov  Jan 17, 2019
 #2
avatar+111357 
+2

tan  A    will be undefned at   pi/2  +  n * pi

 

So    let  A  =    θ/2

 

So      θ /2  =  pi /2  +  n* pi        multiply through by 2

 

So      θ  =   pi  + n*2pi

 

So.....it will  be defined at all real numbers except    pi  +  2pi * n

 

So.... "d"  is correct...

 

cool cool cool

 Jan 17, 2019

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