third quadrant, as x increases from π to π , sin x decreases from to –1and finally, in the fourth quadrant, sin x increases from – to as x increases from π to π . Similarly, we can discuss the behaviour of other trigonometric functions. In fact, we have the following table: Remark In the above table, the statement tan x increases from to ∞ (infinity) for < x < π simply means that tan x increases as x increases for < x < π and I quadrant II quadrant III quadrant IV quadrant sin increases from to decreases from to decreases from to – increases from – to cos decreases from to decreases from to – increases from – to increases from to tan increases from to ∞ increases from – ∞ to increases from to ∞ increases from – ∞ to cot decreases from ∞ to decreases from to– ∞ decreases from ∞ to decreases from 0to – ∞ sec increases from to ∞ increases from – ∞ to– decreases from – to– ∞ decreases from ∞ to cosec decreases from ∞ to increases from to ∞ increases from – ∞ to– decreases from–1to– ∞ MATHEMATICS Fig . Fig .
Fig . Fig . assumes arbitraily large positive values as x approaches to π . Similarly, to say that cosec x decreases from – to – ∞ (minus infinity) in the fourth quadrant means that cosec x decreases for x ∈ ( π , π ) and assumes arbitrarily large negative values as x approaches to π .
The symbols ∞ and – ∞ simply specify certain types of behaviour of functions and variables. We have already seen that values of sin x and cos x repeats after an interval of π . Hence, values of cosec x and sec x will also repeat