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If cos x = – 3/5 , x lies in the third quadrant, find the values of other five trigonometric functions.

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Since cos x = - 3/5 , we have sec x = - 5/3
Now sin2 x + cos2 x = 1, i.e., sin2 x = 1 – cos2 x
or sin2 x = 1 – 9/25 = 16/25
Hence sin x = ± 4/5
Since x lies in third quadrant, sin x is negative. Therefore
sin x = – 4/5
which also gives
cosec x = – 5/4

Further, we have
tan x = sinx/cosx = 4/3 and cot x = cosx/sinx = 3/4 .

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