Question

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

Answer 1

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 .