Domain & Range of Trigonometric Functions
Using the table we can observe that Sin & Cos are defined for all real numbers . Further , we observe that for each real number x , – 1 ≤ sin x ≤ 1 and – 1 ≤ cos x ≤ 1 .
Thus , domain of y = sin x and y = cos x is the set of all real numbers and range is the interval [– 1 , 1 ], i . e ., – 1 ≤ y ≤ 1 .
Graph of Sin x & Cos x is shown . Both repeats after 2π
If we notice the graph of tan x , ire repeats after π . Thus domain of y = tan x is the set { x : x ∈ R and x ≠ ( 2n + 1 ) π / 2 , n ∈ Z } and range is the set of all real numbers .