Trigonometric Function - II

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4. f(x) = cosec x

 since, cosec x = 1/a

 observe the variation of 1/a



Domain = R - \{ n\pi \} , n \in I

 Range = ( - \infty , - 1]\bigcup {[1,\infty )}  or R - ( - 1,1)

 f(x) = cosec x is a periodic function of period 2\pi





5. f(x) = sec x

 since, sec x = 1/b

 observe the variation or change in 1/b
Domain = R - \left\{ {2n\pi + \frac{\pi }{2}} \right\},n \in I

 Range = ( - \infty , - 1]\bigcup {[1,\infty )}  or R - (-1,1)

 f(x) = sec x is a periodic function of period 2\pi





6. f(x) = cot x

 since, cot x = b/a

 observe the variation in b/a

Domain = R - \left\{ {n\pi } \right\},n \in I

 Range = R

 It is a periodic function and repeats its value after every interval of \pi





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