Variation Of Graphs, Periodicity, and Extreme values

Variation Of Graphs, Periodicity, and Extreme values
Variation of trigonometric Ratios
1)    Variation of sinx
    As x increases from to 0 to \(\pi \over 2\)  \(\to\) sinx increases from 0 to 1
    As x incerases from \(\pi \over 2\) to \(\pi\)    \(\to\)sinx  decreases from 1 to 0
    As x increases from \(\pi\)  to  \(3\pi \over 2\) \(\to\)sinx decreases from 0 to -1
    As x increases from \(3\pi \over 2\) to \(2\pi\)  \(\to\)sinx  increases from -1 to 0.
II)    Variation of cos x :
    As x  increases from to 0 to\(\pi \over 2\)   \(\to\)cos x decreases  from 1 to 0
    As x incerases from \(\pi \over 2\) to \(\pi\to\)  cos x  decreases from 0 to -1
    As x increases from \(\pi\) to  \({3\pi \over 2} \to\) cos x  increases from -1to 0
    As x increases from \(3\pi \over 2\) to \(2\pi \to\)  cos x  increases from 0 to 1.
III)    Variation of tanx :
    As x  increases from to 0 to  \({\pi \over 2}\to\)  tan  x  increases  from 0 to \(\infty \)
    As x incerases from \(\pi \over 2\) to \(\pi\) \(\to\) tan x  increases  from -\(\infty \) to 0
    As x increases from \(\pi\) to \({3\pi \over 2}\to\)  tan x  increases from  0 to \(\infty \)
    As x increases from \({3\pi \over 2}\) to \(2\pi\) tan x  increases from -\(\infty \) to 0
Note : Similarly we can obtain the variations of \(\cos ecx,\sec x\)  and cot x.  These vaiations can be easily understood from the graphs.