Graphs of some difficult trigonometric functions - II

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NON-PERIODIC FUNCTIONS:

 1. f(x) = \sin {\sin ^{ - 1}}x

 \sin {\sin ^{ - 1}}x = x

 Domain = [-1,1], (since domain of arcsin(x) is [-1,1])

 Range = [-1,1]



2. f(x) = \cos {\cos ^{ - 1}}x

 \cos {\cos ^{ - 1}}x = x

 Domain = [-1,1], (since domain of arccos(x) is [-1,1])

 Range = [-1,1]



3. f(x) = \tan {\tan ^{ - 1}}x

 \tan {\tan ^{ - 1}}x = x

 Domain = R (since domain of arctan(x) is R )

 Range = R


Students are requested to sketch following graph and observe their domain, range and periodicity.

 1. f(x) = \cot {\cot ^{ - 1}}x

 2. f(x) = \cos ec\cos e{c^{ - 1}}x

 3. f(x) = secse{c^{ - 1}}x

 4. f(x) = {\cot ^{ - 1}}\cot x

 5. f(x) = \cos e{c^{ - 1}}\cos ecx

 6.. f(x) = se{c^{ - 1}}secx

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