Mathematics

Problem

For the three standard trigonometric functions

y=\sin x

y=\cos x

and

y=\tan x

, respond to the following items. a. (i) Define the period of a real-valued function. Hence state the fundamental period of each of the three functions mentioned above. b. (ii) Explain, with reason, why the ranges of

\sin x

and

\cos x

are identical while the range of

\tan x

is different. c. (iii) Describe the complete domain of

\tan x

, making clear reference to the points where the function is not defined.

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