SOLUTION: Find the domain of the function f:\theta \rightarrow \left(\frac{\tan \theta \:\:}{2\sin \theta \:-\cos \theta }\right)

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Question 1183579: Find the domain of the function f:\theta \rightarrow \left(\frac{\tan \theta \:\:}{2\sin \theta \:-\cos \theta }\right)
Answer by ikleyn(52792) About Me  (Show Source):
You can put this solution on YOUR website!
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If the function is  f(t) = tan%28t%29%2F%28sin%28t%29-cos%28t%29%29, then


    (a)  the numerator  tan(t) is defined everywhere except t = pi%2F2+%2B+k%2Api,  k = 0, +/-1, +/-2, . . . 


    (b)  the denominator is defined everywhere and is not zero, except of 

         the points t such that  sin(t) = cos(t),  or  tan(t) = 1,  that are  t = pi%2F4+%2B+k%2Api,  k = 0, +/-1, +/-2, . . . 



THEREFORE, the given function domain is the set of all real numbers except

t = pi%2F2+%2B+k%2Api,  k = 0, +/-1, +/-2, . . .  and  t = pi%2F4+%2B+k%2Api,  k = 0, +/-1, +/-2, . . .

Solved.