Mathematics

Problem

Answer the following with reference to the three basic trigonometric functions

\sin x,\;\cos x

and

\tan x

. a. (i) Define the terms domain and range of a real–valued function. b. (ii) State the domain and the range of each of the functions

\sin x,\;\cos x

and

\tan x

. c. (iii) Justify why the domain of

\tan x

excludes all real numbers of the form

x=(2n+1)\dfrac{\pi}{2},\;n\in\mathbb Z

. Use the definitions of

\sin x,\cos x

on the unit circle to support your reasoning. d. (iv) Write the first two positive real numbers that are excluded from the domain of

\tan x

. Give your answer in terms of

\pi

. Explain briefly why these values are excluded.