after an interval of π . We TRIGONOMETRIC FUNCTIONS shall see in the next section that tan ( π + x ) = tan x . Hence, values of tan x will repeat after an interval of π . Since cot x is reciprocal of tan x , its values will also repeat after an interval of π .
Using this knowledge and behaviour of trigonometic functions, we can sketch the graph of these functions. The graph of these functions are given above: Example If cos x = – , x lies in the third quadrant, find the values of other five trigonometric functions. Solution Since cos x = , we have sec x = Now sin x + cos x = , i.e., sin x = – cos x or sin x = – = Hence sin x = ± Since x lies in third quadrant, sin x is negative. Therefore sin x = – which also gives cosec x = – Fig .
Fig . MATHEMATICS Further, we have tan x = sin cos x = and cot x = cos sin x = . Example If cot x = – , x lies in second quadrant, find the values of other five trigonometric functions. Solution Since cot x = – , we have tan x = – Now sec x = + tan x = + = Hence sec x = ± Since x lies in second quadrant, sec x will be negative.
Therefore sec x = – , which also gives cos x = − Further, we have sin x = tan x cos x = (– ) × (– ) = and cosec x = sin x = . Example Find the value of sin π . Solution We know that values of