The domain of y = cot x is the set { x : x ∈ R and x ≠ n π , n ∈ Z } and the range is the set of all real numbers .
Numerical : If cos x = – 3 / 5 , x lies in the third quadrant , find the values of other five trigonometric fx
Solution : Cos x = Base / Hypotenuse = -3 / 5 p 2 = h 2 – b 2 ( using Pythagoras Theorem ) or p 2 = 5 2 – 3 2 or p = 4
Now , it is given that x lies in 3 rd quadrant , so sin & cos will be negative & tan will be positive .
So sin x = -4 / 5 , cos x = - 3 / 5 & tan x = 4 / 3